All STD 11 - Work,energy,power and collision questions
Newest firstShowing 101–150 of 191 questions
- 101. A ball of mass \(4\, kg\), moving with a velocity of \(10\, ms ^{-1}\), collides with a spring of length \(8\, m\) and force constant \(100\, Nm ^{-1}\). The length of the compressed spring is \(x\, m\). The value of \(x\), to the nearest integer, is ........ . 2021 Medium
- 102. A block moving horizontally on a smooth surface with a speed of \(40\, {ms}^{-1}\) splits into two equal parts. If one of the parts moves at \(60\, {ms}^{-1}\) in the same direction, then the fractional change in the kinetic energy will be \(x: 4\) where \(x=..... .\) 2021 Hard
- 103. A block moving horizontally on a smooth surface with a speed of \(40\, {m} / {s}\) splits into two parts with masses in the ratio of \(1: 2\). If the smaller part moves at \(60\, {m} / {s}\) in the same direction, then the fractional change in kinetic energy is :- 2021 Hard
- 104. A body of mass \(2\, {kg}\) moving with a speed of \(4\, {m} / {s}\). makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is \(\frac{x}{10} \,{m} / {s}\). Then the value of \(x\) is ..... . 2021 Hard
- 105. A body of mass ' \({m}\) ' dropped from a height ' \({h}\) ' reaches the ground with a speed of \(0.8 \sqrt{{gh}}\). The value of workdone by the air-friction is \(.....\,{mgh}\) 2021 Hard
- 106. A body of mass \({M}\) moving at speed \({V}_{0}\) collides elastically with a mass \('m'\) at rest. After the collision, the two masses move at angles \(\theta_{1}\) and \(\theta_{2}\) with respect to the initial direction of motion of the body of mass \({M}\). The largest possible value of the ratio \({M} / {m}\), for which the angles \(\theta_{1}\) and \(\theta_{2}\) will be equal, is : 2021 Hard
- 107. A boy is rolling a \(0.5\, kg\) ball on the frictionless floor with the speed of \(20\, ms ^{-1}\). The ball gets deflected by an obstacle on the way. After deflection it moves with \(5 \%\) of its initial kinetic energy. What is the speed of the ball now ? (in \(ms ^{-1}\)) 2021 Medium
- 108. A bullet of \(10\, {g}\), moving with velocity \(v\), collides head-on with the stationary bob of a pendulum and recoils with velocity \(100 \, {m} / {s}\). The length of the pendulum is \(0.5\, {m}\) and mass of the bob is \(1\, {kg}\). The minimum value of \(v=\) \(....{m} / {s}\) so that the pendulum describes a circle. (Assume the string to be inextensible and \({g}=10\, {m} / {s}^{2}\) )
2021 Hard - 109. A constant Power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time \('t'\) is proportional to 2021 Hard
- 110. A force of \(F=(5 y+20) \hat{j} \,N\) acts on a particle. The work done by this force when the particle is moved from \(y=0 \,m\) to \(y=10 \,{m}\) is \(...\,{J}.\) 2021 Medium
- 111. A large block of wood of mass \(M =5.99\, kg\) is hanging from two long massless cords. A bullet of mass \(m =10\, g\) is fired into the block and gets embedded in it. The (block \(+\) bullet) then swing upwards, their centre of mass rising a vertical distance \(h =9.8\,cm\) before the (block \(+\) bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is: (Take \(g =9.8\, ms ^{-2}\) ) (in \(m/s\))
2021 Hard - 112. A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\)) 2021 Medium
- 113. A rubber ball is released from a height of \(5\, m\) above the floor. It bounces back repeatedly, always rising to \(\frac{81}{100}\) of the height through which it falls. Find the average speed of the ball. (Take \(g =10 ms ^{-2}\) ) (in \(ms ^{-1}\)) 2021 Hard
- 114. A small block slides down from the top of hemisphere of radius \(R=3\, {m}\) as shown in the figure. The height \('h'\) at which the block will lose contact with the surface of the sphere is \(............. \;\;m\). (Assume there is no friction between the block and the hemisphere)
2021 Hard - 115. A small bob tied at one end of a thin string of length \(1\, m\) is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio \(5: 1 .\) The velocity of the bob at the height position is ............. \(m / s\) (Take \(\left.g=10 \,m / s ^{2}\right)\) 2021 Hard
- 116. A uniform chain of length \(3\, meter\) and mass \(3\, {kg}\) overhangs a smooth table with \(2\, meter\) laying on the table. If \(k\) is the kinetic energy of the chain in joule as it completely slips off the table, then the value of \({k}\) is (Take \(\left.g=10\, {m} / {s}^{2}\right)\) 2021 Hard
- 117. An automobile of mass \('m'\) accelerates starting from origin and initially at rest, while the engine supplies constant 10.Power \(P\). The position is given as a function of time by: 2021 Hard
- 118. An engine is attached to a wagon through a shock absorber of length \(1.5\, {m}\). The system with a total mass of \(40,000\, {kg}\) is moving with a speed of \(72\, {kmh}^{-1}\) when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by \(1.0\, {m}\). If \(90\, \%\) of energy of the wagon is lost due to friction, the spring constant is \(....\, \times 10^{5}\, {N} / {m}\) 2021 Hard
- 119. An object of mass \(m _{1}\) collides with another object of mass \(m _{2}\), which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses \(m _{2}: m _{1}\) is 2021 Medium
- 120. As shown in the figure, a particle of mass \(10\) \(kg\) is placed at a point \(A\). When the particle is slightly displaced to its right, it starts moving and reaches the point \(B\). The speed of the particle at \(B\) is \(x\, m / s\). (Take \(\left. g =10\, m / s ^{2}\right)\) The value of \('x'\) to the nearest integer is.........
2021 Medium - 121. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Body \('P'\) having mass \(M\) moving with speed \('u'\) has head-on collision elastically with another body \('Q'\) having mass \('m'\) initially at rest. If \(m< < M,\) body \('Q'\) will have a maximum speed equal to \('2u'\) after collision. Reason \(R\) : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below: 2021 Hard
- 122. Given below is the plot of a potential energy function \(U(x)\) for a system, in which a particle is in one dimensional motion, while a conservative force \(F(x)\) acts on it. Suppose that \(E_{\text {mech }}=8\, {J}\), the incorrect statement for this system is:
2021 Hard - 123. If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be \(...\%\) 2021 Medium
- 124. In a spring gun having spring constant \(100\, {N} / {m}\) a small ball \('B'\) of mass \(100\, {g}\) is put in its barrel (as shown in figure) by compressing the spring through \(0.05\, {m}\). There should be a box placed at a distance \('d'\) on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \(2\, {m}\) above the ground. The value of \(d\) is \(....{m} .\) \(\left(g=10\, {m} / {s}^{2}\right)\)
2021 Hard - 125. The potential energy \((U)\) of a diatomic molecule is a function dependent on \(r\) (interatomic distance) as \(U =\frac{\alpha}{ r ^{10}}-\frac{\beta}{ r ^{5}}-3\) where, \(\alpha\) and \(\beta\) are positive constants. The equilibrium distance between two atoms will be \(\left(\frac{2 \alpha}{\beta}\right)^{\frac{a}{b}},\) where a \(=\) .......... 2021 Hard
- 126. Three objects \(A, B\) and \(C\) are kept in a straight line on a frictionless horizontal surface. The masses of \({A}, {B}\) and \({C}\) are \({m}, 2\, {m}\) and \(2\, {m}\) respectively. \(A\) moves towards \({B}\) with a speed of \(9\) \({m} / {s}\) and makes an elastic collision with it. Thereafter \(B\) makes a completely inelastic collision with \(C.\) All motions occur along same straight line. The final speed of \(C\) is \(....\,{m} / {s}\)
2021 Hard - 127. Two identical blocks \(A\) and \(B\) each of mass \(m\) resting on the smooth horizontal floor are connected by a light spring of natural length \(L\) and spring constant \(K\). A third block \(C\) of mass \(m\) moving with a speed \(v\) along the line joining \(A\) and \(B\) collides with \(A\).The maximum compression in the spring is
2021 Hard - 128. Two particles having masses \(4\, g\) and \(16\, g\) respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is \(n : 2 .\) The value of \(n\) will be ...... . 2021 Medium
- 129. Two persons \(A\) and \(B\) perform same amount of work in moving a body through a certain distance \({d}\) with application of forces acting at angle \(45^{\circ}\) and \(60^{\circ}\) with the direction of displacement respectively. The ratio of force applied by person \(A\) to the force applied by person \(B\) is \(\frac{1}{\sqrt{x}}\). The value of \(x\) is ...... . 2021 Medium
- 130. Two solids \(A\) and \(B\) of mass \(1\, kg\) and \(2\, kg\) respectively are moving with equal linear momentum. The ratio of their kinetic energies \((K.E.)_{ A }:( K.E. )_{ B }\) will be \(\frac{ A }{1},\) so the value of \(A\) will be ..... . 2021 Medium
- 131. A \(60\; HP\) electric motor lifts an elevator having a maximum total load capacity of \(2000\; \mathrm{kg}\). If the frictional force on the elevator is \(4000 \;\mathrm{N}\). the speed of the elevator at full load is close to .............. \(\mathrm{m} / \mathrm{s}\) \(\left(1 \;\mathrm{HP}=746 \;\mathrm{W}, \mathrm{g}=10\; \mathrm{ms}^{-2}\right)\) 2020 Medium
- 132. A block of mass \(1.9\, kg\) is at rest at the edge of a table, of height \(1\, m\). A bullet of mass \(0.1\, kg\) collides with the block and sticks to it. If the velocity of the bullet is \(20\, m / s\) in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is \(....J\) [Take \(g =10\, m / s ^{2}\). Assume there is no rotational motion and loss of energy after the collision is negligable. \(]\) 2020 Medium
- 133. A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is 2020 Medium
- 134. A body \(A\) of mass \(\mathrm{m}\) is moving in a circular orbit of radius \(\mathrm{R}\) about a planet. Another body \(\mathrm{B}\) of mass \(\frac{\mathrm{m}}{2}\) collides with \(\mathrm{A}\) with a velocity which is half \(\left(\frac{\overrightarrow{\mathrm{v}}}{2}\right)\) the instantaneous velocity \(\overrightarrow{\mathrm{v}}\) of \(\mathrm{A}\) The collision is completely inelastic. Then, the combined body 2020 Medium
- 135. A body of mass \(2\, kg\) is driven by an engine delivering a constant 10.Power \(1\, J / s\). The body starts from rest and moves in a straight line. After \(9\) seconds, the body has moved a distance (in \(m )\)
2020 Hard - 136. A cricket ball of mass \(0.15\, kg\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20 \;m\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2\, m\) while launching the ball, the value of \(F(\) in \(N)\) is \(\left(g=10\, m s^{-2}\right)\) 2020 Medium
- 137. A particle \((\mathrm{m}=1\; \mathrm{kg})\) slides down a frictionless track \((AOC)\) starting from rest at a point \(A\) (height \(2\; \mathrm{m}\) ). After reaching \(\mathrm{C}\), the particle continues to move freely in air as a projectile. When it reaching its highest point \(P\) (height \(1 \;\mathrm{m}\) ). the kinetic energy of the particle (in \(\mathrm{J}\) ) is : (Figure drawn is schematic and not to scale; take \(\left.g=10 \;\mathrm{ms}^{-2}\right)\)
2020 Medium - 138. A particle moving in the \(xy\) plane experiences a velocity dependent force \(\overrightarrow{ F }= k \left( v _{ y } \hat{ i }+ v _{ x } \hat{ j }\right),\) where \(v _{ x }\) and \(v _{ y }\) are the \(x\) and \(y\) components of its velocity \(\overrightarrow{ v } .\) If \(\overrightarrow{ a }\) be the acceleration of the particle, then which of the following statements is true for the particle\(?\) 2020 Hard
- 139. A particle of mass \(\mathrm{m}\) is dropped from a height \(h\) above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2 \mathrm{gh}} .\) If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\) is 2020 Hard
- 140. A particle of mass \(m\) is moving along the \(x\) -axis with initial velocity \(u \hat i\). It collides elastically with a particle of mass \(10\, m\) at rest and then moves with half its initial kinetic energy (see figure). If \(\sin \theta_{1}=\sqrt{n} \sin \theta_{2}\) then value of \(n\) is.....
2020 Hard - 141. A particle of mass \(\mathrm{m}\) is projected with a speed \(u\) from the ground at an angle \(\theta=\frac{\pi}{3}\) w.r.t. horizontal (\(x-\)axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity \(u \hat i\). The horizontal distance covered by the combined mass before reaching the ground is 2020 Hard
- 142. A particle of mass \(m\) with an initial velocity \(u\hat i\) collides perfectly elastically with a mass \(3m\) at rest. It moves with a velocity \(v\hat j\) after collision, then, \(v\) is given by 2020 Hard
- 143. A person pushes a box on a rough horizontal platform surface. He applies a force of \(200\, N\) over a distance of \(15\, m .\) Thereafter, he gets progressively tired and his applied force reduces linearly with distance of \(100\, N\). The total distance through which the box has been moved is \(30\, m\). What is the work done by the person during the total movement of the box\(........J\)\(?\) 2020 Hard
- 144. An elevator in a building can carry a maximum of \(10\) persons, with the average mass of each person being \(68\; kg\). The mass of the elevator itself is \(920\; kg\) and it moves with a constant speed \(3\; \mathrm{m} / \mathrm{s}\). The frictional force opposing the motion is \(6000 \;\mathrm{N}\). If the elevator is moving up with its full capacity, the 10.Power delivered by the motor to the elevator \(\left(\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2}\right)\) must be at least .............. \(\mathrm{W}\) 2020 Medium
- 145. Blocks of masses \(m , 2 m , 4 m\) and \(8 m\) are arranged in a line on a frictionless floor. Another block of mass \(m ,\) moving with speed \(v\) along the same line (see figure) ollides with mass \(m\) in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass \(8 m\) starts moving the total energy loss is \(p \%\) of the original energy. Value of \('p'\) is close to
2020 Hard - 146. Consider a force \(\overrightarrow{\mathrm{F}}=-\mathrm{x} \hat{\mathrm{i}}+\mathrm{y} \hat{\mathrm{j}}\). The work done by this force in moving a particle from point \(\mathrm{A}(1,0)\) to \(\mathrm{B}(0,1)\) along the line segment is (all quantities are in \(SI\) units)
2020 Medium - 147. If the potential energy between two molecules is given by \(U =\frac{-A }{ r ^{6}}+\frac{ B }{ r ^{12}},\) then at equilibrium, separation between molecules, and the potential energy are 2020 Hard
- 148. Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is. 2020 Medium
- 149. Two particles of equal mass \(\mathrm{m}\) have respective initial velocities \(u\hat{i}\) and \(u\left(\frac{\hat{\mathrm{i}}+ \hat{\mathrm{j}}}{2}\right) .\) They collide completely inelastically. The energy lost in the process is 2020 Hard
- 150. A block of mass \(m\) is kept on a platform which starts from rest with constant acceleration \(g/2\) upward, as shown in figure. Work done by normal reaction on block in time \(t\) is
2019 Medium
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