An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

Two ideal electric dipoles \(A\) and \(B\) having their dipole moment \(p_{1}\) and \(p_{2}\) respectively are placed on a plane with their centres at \(O\) as shown in the figure. At point \(C\) on the axis of dipole \(A\), the resultant electric field is making an angle of \(37^{\circ}\) with the axis. The ratio of the dipole moment of \(A\) and \(B, \frac{P_{1}}{P_{2}}\) is \(....\) (take \(\left.\sin 37^{\circ}=\frac{3}{5}\right)\)

At very high frequencies, the effective impendance of the given circuit will be \(....\Omega\)

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears \(2\; beats/sec\). The oscillation frequency of each tuning fork is \(v_{0}=1400 \;\mathrm{Hz}\) and the velocity of sound in air is \(350\; \mathrm{m} / \mathrm{s}\). The speed of each tuning fork is close to 

An object is at a distance of \(20\,m\) from a convex lens of focal length \(0.3\,m.\) The lens forms an image of the object. If the object moves away from the lens at a speed of \(5\,m/s,\) the speed and direction of the image will be

Given below are two statement  Statement \(-I\) : What \(\mu\) amount of an ideal gas undergoes adiabatic change from state \(\left( P _{1}, V _{1}, T _{1}\right)\) to state \(\left( P _{2}, V _{2}, T _{2}\right)\), the work done is \(W =\frac{1 R \left( T _{2}- T _{1}\right)}{1-\gamma}\), where \(\gamma=\frac{ C _{ P }}{ C _{ V }}\) and \(R =\) universal gas constant, Statement \(-II\) : In the above case. when work is done on the gas. the temperature of the gas would rise. Choose the correct answer from the options given below

A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)

A metal bal of mass \(0.1\, kg\) is heated upto \(500\,{}^oC\) and dropped into a vessel of heat capacity \(800\, JK^{-1}\) and containing \(0.5\, kg\) water. The initial temperature of water and vessel is \(30\,{}^oC\). ........ \(\%\) is the approximate percentage increment in the temperature of the water. [Specific heat Capacities of water and metal are, respectively \(4200\, Jkg^{-1}K^{-1}\) and \(400\, Jkg^{-1}K^{-1}\)]

The given figure represents two isobaric processes for the same mass of an ideal gas, then ....

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \(\mathrm{R}=2 \mathrm{~m}\). Another car approaches him from behind with a uniform speed of \(90 \mathrm{~km} / \mathrm{hr}\). When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ \(\mathrm{m} / \mathrm{s}^2\).

A ball is thrown upward with an initial velocity \(V_0\) from the surface of the earth. The motion of the ball is affected by a drag force equal to \(m\gamma {v^2}\) (where \(m\) is mass of the ball, \(v\) is its Instantneous velocity and \(\gamma \) is a constant). Time taken by the ball to rise to its zenith is

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

An engine operating between the boiling and freezing points of water will have \(1.\) efficiency more than \(27 \%\) \(2.\) efficiency less than the efficiency a Carnot engine operating between the same two temperatures. \(3.\) efficiency equal to \(27 \%\) \(4.\) efficiency less than \(27 \%\)