Kinematics · JEE Main previous year questions

2023 39 questions

1. Q312023 · 31 Jan 2023 · Shift 1

   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.$\frac{\sqrt{3}u}{g}$
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   Answer: A

2. Q402023 · 31 Jan 2023 · Shift 1

   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.$200mvt$
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   Answer: A

3. Q542023 · 31 Jan 2023 · Shift 1· Numerical answer

   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 ___________ ${\text{km h}}^{-1}$

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   Answer: 3

4. Q482023 · 31 Jan 2023 · Shift 2

   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.$5\pi$
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   Answer: C

5. Q542023 · 31 Jan 2023 · Shift 2· Numerical answer

   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 $g=10{\text{ ms}}^{-2}$ )

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   Answer: 80

6. Q552023 · 31 Jan 2023 · Shift 2· Numerical answer

   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.

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   Answer: 20

7. Q412023 · 29 Jan 2023 · Shift 2

   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.$v=-4\hat{\mathrm{j}}m/s,a=8\hat{\mathrm{i}}m/{\mathrm{s}}^2$
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   Answer: B

8. Q562023 · 29 Jan 2023 · Shift 2· Numerical answer

   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 __________.

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   Answer: 40

9. Q392023 · 25 Jan 2023 · Shift 1

   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.$\frac{v_1+v_2}{2}$
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   Answer: B

10. Q462023 · 25 Jan 2023 · Shift 1

    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.$\frac{\pi }{3}$
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    Answer: C

11. Q392023 · 25 Jan 2023 · Shift 2

    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
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    Answer: A

12. Q602023 · 25 Jan 2023 · Shift 2· Numerical answer

    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.

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    Answer: 400

13. Q322023 · 24 Jan 2023 · Shift 2
    
    1. A.1 : 1
    2. B.1 : 3
    3. C.1 : 4
    4. D.1 : 2
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    Answer: B

14. Q492023 · 24 Jan 2023 · Shift 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
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    Answer: B