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JEE Advanced > Kinematics

Explore popular questions from Kinematics for JEE Advanced. This collection covers Kinematics previous year JEE Advanced questions hand picked by experienced teachers.

Q 1.

Correct4

Incorrect-1

A river is flowing from west to east at a speed of 5 metres per minute, A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

due north

B

{tex} 30 ^ { \circ } {/tex} east of north

C

{tex} 30 ^ { \circ } {/tex} west of north

D

{tex} 60 ^ { \circ } {/tex} east of north

Explanation

Q 2.

Correct4

Incorrect-1

A boat which has a speed of {tex} 5 \mathrm { km } / \mathrm { hr } {/tex} in still water crosses a river of width {tex} 1 \mathrm { km } {/tex} along the shortest possible path in {tex}15{/tex} minutes. The velocity of the river water in {tex} \mathrm { km } / \mathrm { hr } {/tex} is

A

{tex}1{/tex}

{tex}3{/tex}

C

{tex}4{/tex}

D

{tex} \sqrt { 41 } {/tex}

Explanation

Q 3.

Correct4

Incorrect-1

In 1.0{tex}\mathrm { s }{/tex} , a particle goes from point A to point B , moving in a semicircle of radius 1.0{tex}\mathrm { m }{/tex} (see Figure). The magnitude of the average velocity

A

{tex} 3.14 \mathrm { m } / \mathrm { s } {/tex}

{tex} 2.0 \mathrm { m } / \mathrm { s } {/tex}

C

{tex} 1.0 \mathrm { m } / \mathrm { s } {/tex}

D

Zero

Explanation

Q 4.

Correct4

Incorrect-1

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height {tex} d / 2 {/tex}. Neglecting subsequent motion and air resistance, its velocity {tex} v {/tex} varies with the height {tex} h {/tex} above the ground as

B

C

D

Explanation

Q 5.

Correct4

Incorrect-1

A particle starts sliding down a frictionless inclined plane. If {tex} S _ { n } {/tex} is the distance travelled by it from time {tex} t = n - 1 {/tex} sec to {tex} t = n {/tex} sec, the ratio {tex} S _ { n } / S _ { n + 1 } {/tex} is

{tex} \frac { 2 n - 1 } { 2 n + 1 } {/tex}

B

{tex} \frac { 2 n + 1 } { 2 n } {/tex}

C

{tex} \frac { 2 n } { 2 n + 1 } {/tex}

D

{tex} \frac { 2 n + 1 } { 2 n - 1 } {/tex}

Explanation

Q 6.

Correct4

Incorrect-1

A body starts from rest at time {tex} t = 0 {/tex}, the acceleration time graph is shown in the figure. The maximum velocity attained by the body will be

A

{tex} 110 \mathrm { m } / \mathrm { s } {/tex}

{tex} 55 \mathrm { m } / \mathrm { s } {/tex}

C

{tex} 650 \mathrm { m } / \mathrm { s } {/tex}

D

{tex} 550 \mathrm { m } / \mathrm { s } {/tex}

Explanation

Q 7.

Correct4

Incorrect-1

The velocity-displacement graph of a particle moving along a straight line is shown

The most suitable acceleration-displacement graph will be

B

C

D

Explanation


Q 8.

Correct4

Incorrect-1

Two identical discs of same radius {tex} R {/tex} are rotating about their axes in opposite directions with the same constant angular speed {tex} \omega {/tex}. The discs are in the same horizontal plane. At time {tex} t = 0 , {/tex} the points {tex} P {/tex} and {tex} Q {/tex} are facing each other as shown in the figure. The relative speed between the two points {tex} P {/tex} and {tex} Q {/tex} is {tex} v _ { r } {/tex} In one time period (T) of rotation of the discs, {tex} v _ { r } {/tex} as a function of time is best represented by

B

C

D

Explanation

Q 9.

Correct4

Incorrect-1

Consider a disc rotating in the horizontal plane with a constant angular speed m about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles With respect to the disc. Assume that (i) they land back on the before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) {tex} \omega {/tex} remains constant throughout. Then

A

{tex} P {/tex} lands in the shaded region and {tex} Q {/tex} in the unshaded region.

B

{tex} P {/tex} lands in the unshaded region and {tex} Q {/tex} in the shaded region.

Both {tex} P {/tex} and {tex} Q {/tex} land in the unshaded region.

D

Both {tex} P {/tex} and {tex} Q {/tex} land in the shaded region.

Explanation

Q 10.

Correct4

Incorrect-1

Three vectors {tex} \overrightarrow { \mathrm { P } } , \overrightarrow { \mathrm { Q } } {/tex} and {tex} \overrightarrow { \mathrm { R } } {/tex} are shown in the figure. Let {tex} \mathrm { S } {/tex} be anypoint on the vector {tex} \overrightarrow { \mathrm { R } } {/tex}. The distance between the points {tex} \mathrm { P } {/tex} and {tex} \mathrm { S } {/tex} is {tex} \mathrm { b } | \overrightarrow { \mathrm { R } } | {/tex}. The general relation among vectors {tex} \overrightarrow { \mathrm { P } } , \overrightarrow { \mathrm { Q } } {/tex} and {tex} \overrightarrow { \mathrm { S } } {/tex} is

{tex} \overrightarrow { \mathrm { S } } = ( 1 - \mathrm { b } ) \overrightarrow { \mathrm { P } } + \mathrm { b } \overrightarrow { \mathrm { Q } } {/tex}

B

{tex} \overrightarrow { \mathrm { S } } = ( \mathrm b - 1 ) \overrightarrow { \mathrm { P } } + b \overrightarrow { \mathrm { Q } } {/tex}

C

{tex} \overrightarrow { \mathrm { S } } = \left( 1 - \mathrm { b } ^ { 2 } \right) \overrightarrow { \mathrm { P } } + \mathrm { b } \overrightarrow { \mathrm { Q } } {/tex}

D

{tex} \overrightarrow { \mathrm { S } } = ( 1 - \mathrm { b } ) \overrightarrow { \mathrm { P } } + \mathrm { b } ^ { 2 } \overrightarrow { \mathrm { Q } } {/tex}

Explanation

Q 11.

Correct4

Incorrect-1

A train {tex} 100 \mathrm { m } {/tex} long travelling at {tex} 40 \mathrm { ms } ^ { - 1 } {/tex} starts overtaking another train {tex} 200 \mathrm { m } {/tex} long travelling at {tex} 30 \mathrm { ms } ^ { - 1 } {/tex}. The time taken by the first train to pass the second train completely is

{tex} 30 \mathrm { s } {/tex}

B

{tex} 40 \mathrm { s } {/tex}

C

{tex} 50 \mathrm { s } {/tex}

D

{tex} 60 \mathrm { s } {/tex}

Explanation

Q 12.

Correct4

Incorrect-1

Water drops fall from a tap on the floor {tex} 5 \mathrm { m } {/tex} below at regular intervals of time, the first drop striking the floor when the fifth drop begins to fall. The height at which the third drop will be from ground (at the instant when the first drop strikes the ground), will be {tex} \left( \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}

A

{tex} 1.25 \mathrm { m } {/tex}

B

{tex} 2.15 \mathrm { m } {/tex}

C

{tex} 2.75 \mathrm { m } {/tex}

{tex} 3.75 \mathrm { m } {/tex}

Explanation


Q 13.

Correct4

Incorrect-1

The position {tex} x {/tex} of a particle varies with time {tex} ( t ) {/tex} as {tex} x = a t ^ { 2 } - b t ^ { 3 } {/tex}. The acceleration at time {tex} t {/tex} of the particle will be equal to zero, where {tex} t {/tex} is equal to

A

{tex} \frac { 2 a } { 3 b } {/tex}

B

{tex} \frac { a } { b } {/tex}

{tex} \frac { a } { 3 b } {/tex}

D

Zero

Explanation

Q 14.

Correct4

Incorrect-1

An object accelerates from rest to a velocity {tex} 27.5 \mathrm { ms } ^ { - 1 } {/tex} in {tex} 10 \mathrm { s } {/tex}. Find the distance covered by the object during the next {tex} 10 \mathrm { s } {/tex}

{tex} 412.5 \mathrm { m } {/tex}

B

{tex} 137.5 \mathrm { m } {/tex}

C

{tex} 550 \mathrm { m } {/tex}

D

{tex} 275 \mathrm { m } {/tex}

Explanation

Q 15.

Correct4

Incorrect-1

Two balls are dropped from the top of a high tower with a time interval of {tex} t _ { 0 } {/tex} second, where {tex} t _ { 0 } {/tex} is smaller than the time taken by the first ball to reach the floor, which is perfectly inelastic. The distance {tex} s {/tex} between the two balls, plotted against the time lapse {tex} t {/tex} from the instant of dropping the second ball is best represented by

A

B

C

Explanation

Q 16.

Correct4

Incorrect-1

Drops of water fall at regular intervals from roof of a building of height {tex} H = 16 \mathrm { m } , {/tex} the first drop striking the ground at the same moment as the fifth drop detaches itself from the roof. The distance between separate drops in air as the first drop reaches the ground are

A

{tex} 1 \mathrm { m } , 5 \mathrm { m } , 7 \mathrm { m } , 3 \mathrm { m } {/tex}

{tex} 1 \mathrm { m } , 3 \mathrm { m } , 5 \mathrm { m } , 7 \mathrm { m } {/tex}

C

{tex} 1 \mathrm { m } , 3 \mathrm { m } , 7 \mathrm { m } , 5 \mathrm { m } {/tex}

D

None of the above

Explanation


Q 17.

Correct4

Incorrect-1

Which of the following velocity-time graphs shows a realistic situation for a body in motion?

A

C

D

Explanation

Q 18.

Correct4

Incorrect-1

A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is {tex} 1 \mathrm { m } {/tex} long and takes {tex} 1 \mathrm { s } {/tex}. There is a pit on the road {tex} 11 \mathrm { m } {/tex} away from the starting point. The drunkard will fall into the pit after

{tex} 29 \mathrm { s } {/tex}

B

{tex} 21 \mathrm { s } {/tex}

C

{tex} 37 \mathrm { s } {/tex}

D

{tex} 31 \mathrm { s } {/tex}

Explanation

Q 19.

Correct4

Incorrect-1

From a high tower, at time {tex} t = 0 , {/tex} one stone is dropped from rest and simultaneously another stone is projected vertically up with an initial velocity. The graph of distance {tex} S {/tex} between the two stones plotted against time {tex} t {/tex} will be

B

C

D

Explanation

Q 20.

Correct4

Incorrect-1

The distance travelled by a particle in a straight line motion is directly proportional to {tex} t ^ { 1 / 2 } , {/tex} where {tex} t = {/tex} time elapsed. What is the nature of motion?

A

Increasing acceleration

B

Decreasing acceleration

C

Increasing retardation

Decreasing retardation

Explanation

Q 21.

Correct4

Incorrect-1

A particle is projected at an angle of elevation {tex} \alpha {/tex} and after {tex} t {/tex} second, it appears to have an angle of elevation {tex} \beta {/tex} as seen from point of projection. The initial velocity will be

A

{tex} \frac { \mathrm { g } t } { 2 \sin ( \alpha - \beta ) } {/tex}

{tex} \frac { \mathrm { g } t \cos \beta } { 2 \sin ( \alpha - \beta ) } {/tex}

C

{tex} \frac { \sin ( \alpha - \beta ) } { 2 g t } {/tex}

D

{tex} \frac { 2 \sin ( \alpha - \beta ) } { \operatorname { gt } \cos \beta } {/tex}

Explanation

Q 22.

Correct4

Incorrect-1

A plane flying horizontally at {tex} 100 \mathrm { ms } ^ { - 1 } {/tex} releases an object which reaches the ground in {tex} 10 \mathrm { s } {/tex}. At what angle with horizontal it hits the ground?

A

{tex} 55 ^ { \circ } {/tex}

{tex} 45 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

D

{tex} 75 ^ { \circ } {/tex}

Explanation

Q 23.

Correct4

Incorrect-1

A river is flowing from west to east at a speed of {tex} 5 \mathrm { m } / \mathrm { min } {/tex}. A man on the south bank of the river, capable of swimming at {tex} 10 \mathrm { m } / \mathrm { min } {/tex} in still water, wants to swim across the river in the shortest time. Finally he will move in a direction

A

{tex} \tan ^ { - 1 } ( 2 ) \mathrm { E } {/tex} of {tex} \mathrm { N } {/tex}

{tex} \tan ^ { - 1 } ( 2 ) \mathrm { N } {/tex} of {tex} \mathrm { E } {/tex}

C

{tex} 30 ^ { \circ } \mathrm { E } {/tex} of {tex} \mathrm { N } {/tex}

D

{tex} 60 ^ { \circ } \mathrm { E } {/tex} of {tex} \mathrm { N } {/tex}

Explanation

Q 24.

Correct4

Incorrect-1

The trajectory of a projectile in a vertical plane is {tex} y = a x - b x ^ { 2 } , {/tex} where {tex} a {/tex} and {tex} b {/tex} are constants and {tex} x {/tex} and {tex} y {/tex} are, respectively, horizontal and vertical distance of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are

A

{tex} \frac { b ^ { 2 } } { 2 a } , \tan ^ { - 1 } ( b ) {/tex}

B

{tex} \frac { a ^ { 2 } } { b } , \tan ^ { - 1 } ( 2 b ) {/tex}

{tex} \frac { a ^ { 2 } } { 4 b } , \tan ^ { - 1 } ( a ) {/tex}

D

{tex} \frac { 2 a ^ { 2 } } { b } , \tan ^ { - 1 } ( a ) {/tex}

Explanation

Q 25.

Correct4

Incorrect-1

A particle is projected from ground at some angle with the horizontal. Let {tex} P {/tex} be the point at maximum height {tex} H . {/tex} At what height above the point {tex} P {/tex} should the particle be aimed to have range equal to maximum height?

{tex} H {/tex}

B

{tex} 2 H {/tex}

C

{tex} H / 2 {/tex}

D

{tex} 3 H {/tex}

Explanation