Kinematics · JEE Main previous year questions

2022 26 questions

1. Q322022 · 29 Jul 2022 · Shift 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.$\frac{1}{3}$
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   Answer: B

2. Q512022 · 29 Jul 2022 · Shift 1· Numerical answer

   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.

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   Answer: 15 or 75

3. Q372022 · 29 Jul 2022 · Shift 2

   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.$g/2n^2$
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   Answer: D

4. Q332022 · 28 Jul 2022 · Shift 1

   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.
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   Answer: B

5. Q602022 · 28 Jul 2022 · Shift 1· Numerical answer

   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.

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   Answer: 340

6. Q512022 · 28 Jul 2022 · Shift 2· Numerical answer

   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 $g=9.8{\text{ m/s}}^2$)

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   Answer: 392

7. Q532022 · 28 Jul 2022 · Shift 2· Numerical answer

   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 $g=10{\text{ m/s}}^2$)

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   Answer: 30

8. Q332022 · 27 Jul 2022 · Shift 1

   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.$12.5\text{ W}$
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   Answer: D

9. Q582022 · 27 Jul 2022 · Shift 1· Numerical answer

   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 _________ $\mu \text{m}$.

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   Answer: 48

10. Q602022 · 27 Jul 2022 · Shift 1· Numerical answer

    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 _________.

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    Answer: 1

11. Q322022 · 27 Jul 2022 · Shift 2

    A body of mass $10\mathrm{kg}$ is projected at an angle of $45^{\circ }$ with the horizontal. The trajectory of the body is observed to pass through a point $(20,10)$. If $\mathrm{T}$ is the time of flight, then its momentum vector, at time $t=\frac{\mathrm{T}}{\sqrt{2}}$, is ____. $[\text{Take }g=10m/{\mathrm{s}}^2]$

    1. A.$100\hat{i}+(100\sqrt{2}-200)\hat{j}$
    2. B.$100\sqrt{2}\hat{i}+(100-200\sqrt{2})\hat{j}$
    3. C.$100\hat{i}+(100-200\sqrt{2})\hat{j}$
    4. D.$100\sqrt{2}\hat{i}+(100\sqrt{2}-200)\hat{j}$
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    Answer: D

12. Q512022 · 26 Jul 2022 · Shift 1· Numerical answer

    If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y=5x(1-x)$. The $y$ component vector of the initial velocity is ____ $\hat{j}$. (Take $g=10m/{\mathrm{s}}^2$)

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    Answer: 5

13. Q452022 · 25 Jul 2022 · Shift 2

    A ball is projected from the ground with a speed $15{\text{ ms}}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then '$\tan \theta$' will be equal to :

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

14. Q312022 · 30 Jun 2022 · Shift 1

    At $t=0$, truck, starting from rest, moves in the positive x-direction at uniform acceleration of $5\mathrm{m}{\mathrm{s}}^{-2}$. At $t=20\mathrm{s}$, a ball is released from the top of the truck. The ball strikes the ground in $1\mathrm{s}$ after the release. The velocity of the ball, when it strikes the ground, will be : (Given $g=10\mathrm{m}{\mathrm{s}}^{-2}$)

    1. A.$100\hat{i}-10\hat{j}$
    2. B.$10\hat{i}-100\hat{j}$
    3. C.$100\hat{i}$
    4. D.$-10\hat{j}$
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    Answer: A

15. Q342022 · 30 Jun 2022 · Shift 1

    Two projectiles ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ thrown with speed in the ratio $\sqrt{3}:\sqrt{2}$, attain the same height during their motion. If ${\mathrm{P}}_2$ is thrown at an angle of $60^{\circ }$ with the horizontal, the angle of projection of ${\mathrm{P}}_1$ with horizontal will be :

    1. A.$15^{\circ }$
    2. B.$30^{\circ }$
    3. C.$45^{\circ }$
    4. D.$60^{\circ }$
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    Answer: C

16. Q512022 · 30 Jun 2022 · Shift 1· Numerical answer
    
    Show answer

    Answer: 3

17. Q602022 · 28 Jun 2022 · Shift 2· Numerical answer

    A car covers AB distance with first one-third at velocity ${\mathrm{v}}_1\mathrm{m}{\mathrm{s}}^{-1}$, second one-third at ${\mathrm{v}}_2\mathrm{m}{\mathrm{s}}^{-1}$ and last one-third at ${\mathrm{v}}_3\mathrm{m}{\mathrm{s}}^{-1}$. If ${\mathrm{v}}_3=3{\mathrm{v}}_1$, ${\mathrm{v}}_2=2{\mathrm{v}}_1$ and ${\mathrm{v}}_1=11\mathrm{m}{\mathrm{s}}^{-1}$ then the average velocity of the car is ____ $\mathrm{m}{\mathrm{s}}^{-1}$.

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    Answer: 18

18. Q312022 · 27 Jun 2022 · Shift 1

    A projectile is launched at an angle '$\alpha$' with the horizontal with a velocity $20\mathrm{m}{\mathrm{s}}^{-1}$. After $10\mathrm{s}$, its inclination with horizontal is '$\beta$'. The value of $\tan \beta$ will be : ($g=10\mathrm{m}{\mathrm{s}}^{-2}$).

    1. A.$\tan \alpha +5\sec \alpha$
    2. B.$\tan \alpha -5\sec \alpha$
    3. C.$2\tan \alpha -5\sec \alpha$
    4. D.$2\tan \alpha +5\sec \alpha$
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    Answer: B

19. Q322022 · 27 Jun 2022 · Shift 1

    A girl standing on road holds her umbrella at $45^{\circ }$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}\mathrm{km}{\mathrm{h}}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

    1. A.$30\mathrm{km}{\mathrm{h}}^{-1}$
    2. B.$\frac{25}{\sqrt{2}}\mathrm{km}{\mathrm{h}}^{-1}$
    3. C.$\frac{30}{\sqrt{2}}\mathrm{km}{\mathrm{h}}^{-1}$
    4. D.$25\mathrm{km}{\mathrm{h}}^{-1}$
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    Answer: C

20. Q332022 · 26 Jun 2022 · Shift 1

    An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

    1. A.Momentum
    2. B.Potential Energy
    3. C.Acceleration
    4. D.Force
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    Answer: A

21. Q462022 · 26 Jun 2022 · Shift 2

    For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

    1. A.$3\times 10^8{\text{ ms}}^{-1}$
    2. B.$3\times 10^{10}{\text{ ms}}^{-1}$
    3. C.$3.13\times 10^5{\text{ ms}}^{-1}$
    4. D.$4.48\times 10^5{\text{ ms}}^{-1}$
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    Answer: C

22. Q362022 · 25 Jun 2022 · Shift 1

    The terminal velocity ($v_{\mathrm{t}}$) of the spherical rain drop depends on the radius ($r$) of the spherical rain drop as :

    1. A.$r^{1/2}$
    2. B.$r$
    3. C.$r^2$
    4. D.$r^3$
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    Answer: C

23. Q312022 · 25 Jun 2022 · Shift 2

    Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. If A and B reached the maximum height $h_1$ and $h_2$ respectively, then $R=4\sqrt{h_1{h}_2}$ Reason R : Product of said heights. $h_1{h}_2=\left(\frac{u^2{\sin }^2\theta }{2g}\right)\cdot \left(\frac{u^2{\cos }^2\theta }{2g}\right)$ Choose the correct answer :

    1. A.Both A and R are true and R is the correct explanation of A.
    2. B.Both A and R are true but R is NOT the correct explanation of A.
    3. C.A is true but R is false.
    4. D.A is false but R is true.
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    Answer: A

24. Q372022 · 25 Jun 2022 · Shift 2

    For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $\mathrm{P}(R,\theta )$ on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed) :

    1. A.$-\frac{v^2}{R}\sin \theta \hat{i}+\frac{v^2}{R}\cos \theta \hat{j}$
    2. B.$-\frac{v^2}{R}\cos \theta \hat{i}+\frac{v^2}{R}\sin \theta \hat{j}$
    3. C.$-\frac{v^2}{R}\cos \theta \hat{i}-\frac{v^2}{R}\sin \theta \hat{j}$
    4. D.$-\frac{v^2}{R}\hat{i}+\frac{v^2}{R}\hat{j}$
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    Answer: C

25. Q452022 · 24 Jun 2022 · Shift 2

    A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

    1. A.$\frac{\rho q{R}^2}{4{\epsilon }_0}$
    2. B.$\frac{\rho q{R}^2}{2{\epsilon }_0}$
    3. C.$\frac{q\rho }{4{\epsilon }_0{R}^2}$
    4. D.$\frac{4{\epsilon }_0{R}^2}{q\rho }$
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    Answer: A