JEE Mains · Physics · STD 11 - 3.2 motion in plane
A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)
- A \(80\)
- B \(800\)
- C \(8\)
- D \(0.8\)
Answer & Solution
Correct Answer
(B) \(800\)
Step-by-step Solution
Detailed explanation
\(\text { Use } \Delta L =\int \limits_0^{ t } \tau dt\) \(L _0=\int \limits_0^2 mg \left( v _{ x } t \right) dt\) \(= mg _{ x } \frac{ t ^2}{2}=(0.1)(10)(10 \sqrt{2}) \frac{2^2}{2}\) \(=20 \sqrt{2}\) \(=\sqrt{800}\,kgm ^2 / s\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A plane electromagnetic wave of frequency \(500\, MHz\) is travelling in vacuum along \(y-\)direction. At a particular point in space and time, \(\overrightarrow{ B }=8.0 \times 10^{-8} \hat{ z } \;T\). The value of electric field at this point is (speed of light \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\) \(\hat{ x }, \hat{ y }, \hat{ z }\) are unit vectors along \(x , y\) and \(z\) direction.JEE Mains 2021 Medium
- An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii \(r_e,r_p\) and \({r_\alpha }\) respectively in a uniform magnetic field \(B\). The relation between \(r_e,r_p\) and \(\;{r_\alpha }\) isJEE Mains 2018 Medium
- Choose the incorrect statement : \((a)\) The electric lines of force entering into a Gaussian surface provide negative flux. \((b)\) A charge ' \(q\) ' is placed at the centre of a cube. The flux through all the faces will be the same. \((c)\) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. \((d)\) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given belowJEE Mains 2021 Medium
- The surface of water in a water tank of cross section area \(750\,cm ^2\) on the top of a house is \(h m\). above the tap level. The speed of water coming out through the tap of cross section area \(500\,mm ^2\) is \(30\,cm / s\). At that instant, \(\frac{d h}{d t}\) is \(x \times 10^{-3} m / s\). The value of \(x\) will be \(.............\).JEE Mains 2023 Medium
- Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure) . Through a hole of radius \(r\) \((r << R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x.\) Then
JEE Mains 2016 Hard - A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)
JEE Mains 2023 Medium
More PYQs from JEE Mains
- The half-life of \(Au ^{198}\) is \(2.7\, days.\) The activity of \(1.50\, mg\) of \(Au ^{198}\) if its atomic weight is \(198\, g mol ^{-1}\) is .......\(Ci\) \(\left( N _{ A }=6 \times 10^{23}\, / mol \right)\)JEE Mains 2021 Hard
- A body is dropped on ground from a height \(h_1\) and after hitting the ground, it rebounds to a height \(h _2\) If the ratio of velocities of the body just before and after hitting ground is \(4\), then percentage loss in kinetic energy of the body is \(\frac{x}{4}\). The value of \(x\) is \(.......\)JEE Mains 2023 Hard
- A \(200\,\Omega \) resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be .............. \(\Omega\)JEE Mains 2019 Medium
- A fair die is tossed repeatedly until a six is obtained. Let \(\mathrm{X}\) denote the number of tosses required and let \(\mathrm{a}=\mathrm{P}(\mathrm{X}=3), \mathrm{b}=\mathrm{P}(\mathrm{X} \geq 3)\) and \(\mathrm{c}=\) \(\mathrm{P}(\mathrm{X} \geq 6 \mid \mathrm{X}>3)\). Then \(\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}\) is equal toJEE Mains 2024 Hard
- The angle of elevation of the top of a vertical tower from a point \(A\), due east of it is \(45^o\) . The angle of elevation of the top of the same tower from a point \(B\). due south of \(A\) is \(30^o\). If the distance between \(A\) and \(B\) is \(54\sqrt 2 \,m\), then the height of the tower (in metres), isJEE Mains 2016 Hard
- If the co-efficient of \(x^9\) in \(\left(\alpha x^3+\frac{1}{\beta x}\right)^{11}\) and the co-efficient of \(x^{-9}\) in \(\left(\alpha x-\frac{1}{\beta x^3}\right)^{11}\) are equal, then \((\alpha \beta)^2\) is equal to \(.............\).JEE Mains 2023 Hard