Kinematics · JEE Main previous year questions

1. A.$\pi r,3r$
2. B.$2r,3\pi r$
3. C.$3\pi r,2r$
4. D.$3\pi r,\pi r$

1. A.$3P_0{\mathrm{V}}_0$
2. B.$-3P_0{\mathrm{V}}_0$
3. C.$-4P_0{\mathrm{V}}_0$
4. D.$4P_0{\mathrm{V}}_0$

A particle is projected at an angle of $30^{\circ }$ from horizontal at a speed of $60\text{ m/s}$. The height traversed by the particle in the first second is $h_0$ and height traversed in the last second, before it reaches the maximum height, is $h_1$. The ratio $h_0:h_1$ is _________. [Take, $g=10{\text{ m/s}}^2$ ]

A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $v=\alpha \sqrt{x}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x=0$ to $x=\mathrm{d}$, will be :

1. A.$\frac{\mathrm{m}}{2{\alpha }^2\mathrm{d}}$
2. B.$\frac{\mathrm{md}}{2{\alpha }^2}$
3. C.$\frac{\mathrm{m}{\alpha }^2\mathrm{d}}{2}$
4. D.$2\mathrm{m}{\alpha }^2\mathrm{d}$

A particle moving in a straight line covers half the distance with speed $6\text{ m/s}$. The other half is covered in two equal time intervals with speeds $9\text{ m/s}$ and $15\text{ m/s}$ respectively. The average speed of the particle during the motion is :

1. A.$9.2\text{ m/s}$
2. B.$8.8\text{ m/s}$
3. C.$10\text{ m/s}$
4. D.$8\text{ m/s}$

Two cars are travelling towards each other at speed of $20\mathrm{m}{\mathrm{s}}^{-1}$ each. When the cars are $300\mathrm{m}$ apart, both the drivers apply brakes and the cars retard at the rate of $2\mathrm{m}{\mathrm{s}}^{-2}$. The distance between them when they come to rest is :

1. A.$25\mathrm{m}$
2. B.$100\mathrm{m}$
3. C.$50\mathrm{m}$
4. D.$200\mathrm{m}$

1. A.$-20\mathrm{J}$
2. B.$205\mathrm{J}$
3. C.$225\mathrm{J}$
4. D.$20\mathrm{J}$

The angle of projection for a projectile to have same horizontal range and maximum height is :

1. A.${\tan }^{-1}\left(\frac{1}{2}\right)$
2. B.${\tan }^{-1}(2)$
3. C.${\tan }^{-1}\left(\frac{1}{4}\right)$
4. D.${\tan }^{-1}(4)$

A body of mass $\mathrm{M}$ thrown horizontally with velocity $\mathrm{v}$ from the top of the tower of height $\mathrm{H}$ touches the ground at a distance of $100\mathrm{m}$ from the foot of the tower. A body of mass $2\mathrm{M}$ thrown at a velocity $\frac{\mathrm{v}}{2}$ from the top of the tower of height $4\mathrm{H}$ will touch the ground at a distance of ____ $\mathrm{m}$.

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n=$ ________.

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

1. A.$t^{2/3}$
2. B.$t^{3/2}$
3. C.$t$
4. D.$t^2$

A particle moves in $x$-$y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{\mathrm{p}}(\mathrm{t})=\hat{i}\cos (\mathrm{kt})-\hat{j}\sin (\mathrm{kt})$. If $\mathrm{k}$ is constant, the angle between $\vec{\mathrm{F}}$ and $\vec{\mathrm{p}}$ will be :

1. A.$\frac{\pi }{2}$
2. B.$\frac{\pi }{3}$
3. C.$\frac{\pi }{4}$
4. D.$\frac{\pi }{6}$

The maximum height reached by a projectile is $64\mathrm{m}$. If the initial velocity is halved, the new maximum height of the projectile is ____ $\mathrm{m}$.

1. A.
2. B.
3. C.
4. D.

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reach upto maximum heights $h_1$ and $h_2$ respectively, above the initial level. The ratio $h_1:h_2$ is $\frac{n}{10}$. The value of $n$ is ____.

1. A.$\sqrt{8}\text{ km}$
2. B.$4\text{ km}$
3. C.$6\text{ km}$
4. D.$8\text{ km}$

1. A.$10.6\text{ m/s}$
2. B.$19.8\text{ m/s}$
3. C.$16.7\text{ m/s}$
4. D.$21.9\text{ m/s}$

A particle moving in a circle of radius $\mathrm{R}$ with uniform speed takes time $\mathrm{T}$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4R$. The angle of projection $\theta$ is then given by :

1. A.${\sin }^{-1}{\left[\frac{2\mathrm{g}{\mathrm{T}}^2}{{\pi }^2\mathrm{R}}\right]}^{\frac{1}{2}}$
2. B.${\sin }^{-1}{\left[\frac{{\pi }^2\mathrm{R}}{2\mathrm{g}{\mathrm{T}}^2}\right]}^{\frac{1}{2}}$
3. C.${\cos }^{-1}{\left[\frac{\pi \mathrm{R}}{2\mathrm{g}{\mathrm{T}}^2}\right]}^{\frac{1}{2}}$
4. D.${\cos }^{-1}{\left[\frac{2\mathrm{g}{\mathrm{T}}^2}{{\pi }^2\mathrm{R}}\right]}^{\frac{1}{2}}$

Train A is moving along two parallel rail tracks towards north with speed $72\text{ km/h}$ and train B is moving towards south with speed $108\text{ km/h}$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $\mathrm{m}{\mathrm{s}}^{-1}$) :

1. A.-50 and -30
2. B.-50 and 30
3. C.-30 and 50
4. D.50 and -30

One end of a metal wire is fixed to a ceiling and a load of $2\text{ kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1\text{ kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________ . $[\text{Area of cross section of wire}=0.005{\text{ cm}}^2,\mathrm{Y}=2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}\text{ and }g=10{\text{ ms}}^{-2}]$

1. A.
2. B.
3. C.
4. D.

A body starts falling freely from height $H$ hits an inclined plane in its path at height $h$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which the body will take the maximum time to reach the ground is ____.

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1)\text{s}$ are $125\text{ m}$ and $50\text{ m/s}$, respectively. The distance travelled by the particle in $(t+2{)}^{\text{th}}\text{s}$ is _________ m.

If the radius of curvature of the path of two particles of same mass are in the ratio $3:4$, then in order to have constant centripetal force, their velocities will be in the ratio of :

1. A.$1:\sqrt{3}$
2. B.$2:\sqrt{3}$
3. C.$\sqrt{3}:2$
4. D.$\sqrt{3}:1$

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p-1)$ seconds and $S_2$ in first $p$ seconds. The displacement ${\text{S}}_1+{\text{S}}_2$ will be made in time :

1. A.$(2p+1)s$
2. B.$(2p-1)s$
3. C.$(2p^2-2p+1)s$
4. D.$\sqrt{(2p^2-2p+1)}s$