Kinematics · JEE Main previous year questions

A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k}\text{ N}$. The value of work done will be ________ $\text{J}$.

The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is :

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

100 balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t\text{ s}$. The total force exerted by the balls on the wall is

1. A.$\frac{200mv}{t}$
2. B.$\frac{100mv}{t}$
3. C.$\frac{mv}{100t}$
4. D.$200mvt$

The speed of a swimmer is $4{\text{ km h}}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $1\text{ km}$, he reaches a point $750\text{ m}$ down the stream on the opposite bank. The speed of the river water is ___________ ${\text{km h}}^{-1}$

A body is moving with constant speed, in a circle of radius $10\text{ m}$. The body completes one revolution in $4\text{ s}$. At the end of 3rd second, the displacement of body (in m ) from its starting point is :

1. A.$15\pi$
2. B.$30$
3. C.$10\sqrt{2}$
4. D.$5\pi$

Two bodies are projected from ground with same speeds $40{\text{ ms}}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ }$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ___________ m. (Given $g=10{\text{ ms}}^{-2}$ )

The displacement equations of two interfering waves are given by $y_1=10\sin \left(\omega t+\frac{\pi }{3}\right)\text{cm}$, $y_2=5[\sin \omega t+\sqrt{3}\cos \omega t]\text{cm}$ respectively. The amplitude of the resultant wave is ___________ cm.

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $x=+2\mathrm{m}$, its velocity is $-4\hat{\mathrm{j}}$ m/s. The object's velocity (v) and acceleration (a) at $x=-2\mathrm{m}$ will be

1. A.$v=4\hat{\mathrm{i}}m/s,a=8\hat{\mathrm{j}}m/{\mathrm{s}}^2$
2. B.$v=4\hat{\mathrm{j}}m/s,a=8\hat{\mathrm{i}}m/{\mathrm{s}}^2$
3. C.$v=-4\hat{\mathrm{i}}m/s,a=-8\hat{\mathrm{j}}m/{\mathrm{s}}^2$
4. D.$v=-4\hat{\mathrm{j}}m/s,a=8\hat{\mathrm{i}}m/{\mathrm{s}}^2$

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $t(1-e^{-\pi /2})\text{s}$. The value of t is __________.

A car travels a distance of '$x$' with speed $v_1$ and then same distance '$x$' with speed $v_2$ in the same direction. The average speed of the car is :

1. A.$\frac{v_1{v}_2}{2(v_1+v_2)}$
2. B.$\frac{2v_1{v}_2}{v_1+v_2}$
3. C.$\frac{2x}{v_1+v_2}$
4. D.$\frac{v_1+v_2}{2}$

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take $g=10m/{\mathrm{s}}^2$)

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

Two objects are projected with same velocity 'u' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha +\beta =90^{\circ }$, the ratio of horizontal range of the first object to the 2nd object will be :

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

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 $\mathrm{m}{\mathrm{s}}^{-1}$) ____ Hz.

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

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be :

1. A.1 : 2
2. B.2 : 3
3. C.2 : 5
4. D.1 : 1

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $\mathrm{h}$. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.

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

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the cases. The value of the angle of projection, at which the second object is projected, will be ____ degree.

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

1. A.$g/2n$
2. B.$g/n$
3. C.$2gn$
4. D.$g/2n^2$

In two different experiments, an object of mass $5\mathrm{kg}$ moving with a speed of $25\mathrm{m}{\mathrm{s}}^{-1}$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

1. A.Impulse and average force acting on the object will be same for both the cases.
2. B.Impulse will be same for both the cases but the average force will be different.
3. C.Average force will be same for both the cases but the impulse will be different.
4. D.Average force and impulse will be different for both the cases.

The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

A ball is thrown vertically upwards with a velocity of $19.6{\text{ ms}}^{-1}$ from the top of a tower. The ball strikes the ground after $6\text{ s}$. The height from the ground up to which the ball can rise will be $(\frac{k}{5})\text{m}$. The value of k is _________. (use $g=9.8{\text{ m/s}}^2$)

A string of area of cross-section $4{\text{ mm}}^2$ and length $0.5\text{ m}$ is connected with a rigid body of mass $2\text{ kg}$. The body is rotated in a vertical circular path of radius $0.5\text{ m}$. The body acquires a speed of $5\text{ m/s}$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ $\times 10^{-5}$. (use Young's modulus $10^{11}{\text{ N/m}}^2$ and $g=10{\text{ m/s}}^2$)

Sand is being dropped from a stationary dropper at a rate of $0.5{\text{ kgs}}^{-1}$ on a conveyor belt moving with a velocity of $5{\text{ ms}}^{-1}$. The power needed to keep the belt moving with the same velocity will be :

1. A.$1.25\text{ W}$
2. B.$2.5\text{ W}$
3. C.$6.25\text{ W}$
4. D.$12.5\text{ W}$

A square aluminum (shear modulus is $25\times 10^9{\text{ Nm}}^{-2}$) slab of side $60\text{ cm}$ and thickness $15\text{ cm}$ is subjected to a shearing force (on its narrow face) of $18.0\times 10^4\text{ N}$. The lower edge is riveted to the floor. The displacement of the upper edge is _________ $\mu \text{m}$.

A ball of mass m is thrown vertically upward. Another ball of mass $2\text{ m}$ is thrown at an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of x is _________.