Kinematics · JEE Main previous year questions

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are $5\mathrm{s}$ and $10\mathrm{s}$, respectively, then the value of $R$ is ____ $\mathrm{m}$. (Take $g=10m/{\mathrm{s}}^2$)

1. A.$250$
2. B.$25$
3. C.$500$
4. D.$125$

The rain drop of mass $1\mathrm{g}$, starts with zero velocity from a height of $1\mathrm{km}$. It hits the ground with a speed of $5m/s$. The work done by the unknown resistive force is ____ $\mathrm{J}$. (take $g=10m/{\mathrm{s}}^2$)

1. A.$-8.75$
2. B.$-8.35$
3. C.$-9.55$
4. D.$-9.98$

A body of mass $1\mathrm{kg}$ moves along a straight line with a velocity $v=2x^2$. The work done by the body during displacement from $x=0$ to $5\mathrm{m}$ is ____ $\mathrm{J}$.

1. A.$0$
2. B.$250$
3. C.$1250$
4. D.$1000$

Two identical bodies A and B of equal masses have initial velocities ${\vec{v}}_1=4\hat{i}\text{ m/s}$ and ${\vec{v}}_2=4\hat{j}\text{ m/s}$ respectively. The body A has acceleration ${\vec{a}}_1=6\hat{i}+6\hat{j}{\text{ m/s}}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ________ path.

1. A.circular
2. B.parabolic
3. C.straight line
4. D.elliptical

A cube has side length $5\mathrm{cm}$ and modulus of rigidity $10^{5}N/{\mathrm{m}}^2$. The displacement produced by a force of $10\mathrm{N}$ in the upper face of cube is ____ $\mathrm{mm}$.

1. A.$25\mathrm{m}$ and zero
2. B.$50\mathrm{m}$ and zero
3. C.$100\mathrm{m}$ and zero
4. D.$100\mathrm{m}$ and $2.5m/s$

1. A.solid cylinder
2. B.ring
3. C.disc
4. D.solid sphere

The two projectiles are projected with the same initial velocities at the $15^{\circ }$ and $30^{\circ }$ with respect to the horizontal. The ratio of their ranges is $1:x$. The value of $x$ is

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

If $x$ and $y$ coordinates of a projectile as a function of time ($t$) are given as $24t$ and $43.6t-4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t=2\mathrm{s}$ is ____.

1. A.60
2. B.45
3. C.30
4. D.75

1. A.$+\frac{1}{3a}$
2. B.$-\frac{1}{a}$
3. C.$\frac{1}{2a}$
4. D.$-\frac{1}{3a}$

A boy throws a ball into air at $45^{\circ }$ from the horizontal to land it on a roof of a building of height $H$. If the ball attains maximum height in $2\mathrm{s}$ and lands on the building in $3\mathrm{s}$ after launch, then value of $H$ is ____ m. $\left(g=10m/{\mathrm{s}}^2\right)$

1. A.20
2. B.25
3. C.10
4. D.15

Sixty four rain drops of radius $1\mathrm{mm}$ each falling down with a terminal velocity of $10cm/s$ coalesce to form a bigger drop. The terminal velocity of bigger drop is ____ $cm/s$.

1. A.$\frac{1}{5}$
2. B.$\frac{2-\sqrt{3}}{5}$
3. C.$\frac{3}{5}$
4. D.$\frac{2+\sqrt{3}}{5}$

A projectile is thrown upward at an angle $60^{\circ }$ with the horizontal. The speed of the projectile is $20m/s$ when its direction of motion is $45^{\circ }$ with the horizontal. The initial speed of the projectile is ____ $m/s$.

1. A.$20\sqrt{3}$
2. B.$20\sqrt{2}$
3. C.40
4. D.$40\sqrt{2}$

A body of mass 2 kg is moving along $x$-direction such that its displacement as function of time is given by $x(t)=\alpha t^2+\beta t+\gamma$ m, where $\alpha =1m/s^2,\beta =1m/s$ and $\gamma =1m$. The work done on the body during the time interval $t=2s$ to $t=3s$, is ____ J.

1. A.42
2. B.24
3. C.49
4. D.12

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ______ and ______ respectively.

1. A.20 s and 100 m
2. B.40 s and 100 m
3. C.40 s and 200 m
4. D.40 s and 0 m

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_1$ and $T_2$ are the total flying times of first and second ball, respectively, then the ratio of $T_1$ and $T_2$ is

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

A body of mass $2\mathrm{kg}$ moving with velocity of ${\vec{v}}_{in}=3\hat{i}+4\hat{j}{\mathrm{ms}}^{-1}$ enters into a constant force field of $6\mathrm{N}$ directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ seconds, then velocity of the body when it emerges from force field is.

1. A.$3\hat{i}+4\hat{j}+\sqrt{5}\hat{k}$
2. B.$4\hat{i}+3\hat{j}+5\hat{k}$
3. C.$3\hat{i}+4\hat{j}-5\hat{k}$
4. D.$3\hat{i}+4\hat{j}+5\hat{k}$

Displacement of a wave is expressed as $x(t)=5\cos \left(628t+\frac{\pi }{2}\right)\mathrm{m}$. The wavelength of the wave when its velocity is $300m/s$ is : $(\pi =3.14)$

1. A.$0.33\mathrm{m}$
2. B.$0.5\mathrm{m}$
3. C.$3\mathrm{m}$
4. D.$5\mathrm{m}$

1. A.(B), (C), (D) only
2. B.(B), (D), (E) only
3. C.(A), (D), (E) only
4. D.(B), (C), (E) only

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

A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n{u}^2}{25g}$, where value of $n$ is: (Given, '$g$' is the acceleration due to gravity.)

1. A.$6$
2. B.$12$
3. C.$18$
4. D.$24$

A river is flowing from west to east direction with speed of $9{\text{ km h}}^{-1}$. If a boat capable of moving at a maximum speed of $27{\text{ km h}}^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^{\circ }$ to direction of river flow, then the width of the river is :

1. A.112.5 m
2. B.75 m
3. C.300 m
4. D.$112.5\times \sqrt{3}\text{ m}$

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\frac{3}{2}x$ distance. The average velocity in this motion is $\frac{50}{7}\text{ m/s}$. If $v_1$ is $5\text{ m/s}$ then $v_2=$ _________ $\text{m/s}$.

A sinusoidal wave of wavelength $7.5\mathrm{cm}$ travels a distance of $1.2\mathrm{cm}$ along the $x$-direction in $0.3\sec$ . The crest P is at $x=0$ at $t=0\sec$ and maximum displacement of the wave is $2\mathrm{cm}$ . Which equation correctly represents this wave?

1. A.$y=2\cos (0.83x-3.35t)\mathrm{cm}$
2. B.$y=2\sin (0.83x-3.5t)\mathrm{cm}$
3. C.$y=2\cos (0.13x-0.5t)\mathrm{cm}$
4. D.$y=2\cos (3.35x-0.83t)\mathrm{cm}$