Kinematics · JEE Main previous year questions

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2023 39 questions

Q432023 · 13 Apr 2023 · Shift 1
Two trains 'A' and 'B' of length ' $l$ ' and ' $4 l$ ' are travelling into a tunnel of length ' $L$ ' in parallel tracks from opposite directions with velocities $108 km/h$ and $72 km/h$ , respectively. If train 'A' takes $35 s$ less time than train 'B' to cross the tunnel, then length ' $L$ ' of tunnel is : (Given $L = 60 l$ )
1. A. $900 m$
2. B. $1200 m$
3. C. $1800 m$
4. D. $2700 m$
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Answer: C
Q472023 · 13 Apr 2023 · Shift 1
A body of mass $(5 \pm 0.5) kg$ is moving with a velocity of $(20 \pm 0.4) m/s$ . Its kinetic energy will be
1. A. $(1000 \pm 140) J$
2. B. $(500 \pm 0.14) J$
3. C. $(1000 \pm 0.14) J$
4. D. $(500 \pm 140) J$
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Answer: A
Q482023 · 13 Apr 2023 · Shift 2
A passenger sitting in a train A moving at $90 km/h$ observes another train B moving in the opposite direction for $8 s$ . If the velocity of the train B is $54 km/h$ , then length of train B is:
1. A. $80 m$
2. B. $200 m$
3. C. $120 m$
4. D. $320 m$
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Answer: D
Q432023 · 12 Apr 2023 · Shift 1
A ball is thrown vertically upward with an initial velocity of $150 m/s$ . The ratio of velocity after $3 s$ and $5 s$ is $\frac{x + 1}{x}$ . The value of $x$ is _________. ${take, g = 10 m/s^{2}}$
1. A. $- 5$
2. B. $10$
3. C. $5$
4. D. $6$
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Answer: C
Q452023 · 11 Apr 2023 · Shift 1
1. A.1
2. B. $\frac{3}{5}$
3. C. $\frac{1}{2}$
4. D. $\frac{5}{3}$
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Answer: D
Q532023 · 11 Apr 2023 · Shift 1· Numerical answer
A projectile fired at $3 0^{\circ}$ to the ground is observed to be at same height at time $3 s$ and $5 s$ after projection, during its flight. The speed of projection of the projectile is _________ $m s^{- 1}$ . (Given $g = 10 m s^{- 2}$ )
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Answer: 80
Q552023 · 11 Apr 2023 · Shift 1· Numerical answer
A force $F = (2 + 3 x) \hat{i}$ acts on a particle in the $x$ direction where F is in newton and $x$ is in meter. The work done by this force during a displacement from $x = 0$ to $x = 4 m$ , is _________ J.
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Answer: 32
Q422023 · 11 Apr 2023 · Shift 2
A projectile is projected at $3 0^{\circ}$ from horizontal with initial velocity $40 ms^{- 1}$ . The velocity of the projectile at $t = 2 s$ from the start will be : (Given $g = 10 m/s^{2}$ )
1. A. $203 ms^{- 1}$
2. B.Zero
3. C. $20 ms^{- 1}$
4. D. $403 ms^{- 1}$
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Answer: A
Q432023 · 11 Apr 2023 · Shift 2
A body of mass $500 g$ moves along $x$ -axis such that its velocity varies with displacement $x$ according to the relation $v = 10 x m/s$ the force acting on the body is:-
1. A. $166 N$
2. B. $5 N$
3. C. $25 N$
4. D. $125 N$
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Answer: C
Q372023 · 10 Apr 2023 · Shift 1
The range of the projectile projected at an angle of $1 5^{\circ}$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of $4 5^{\circ}$ with horizontal, then its range will be
1. A. $502 m$
2. B. $100 m$
3. C. $1002 m$
4. D. $50 m$
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Answer: B
Q382023 · 10 Apr 2023 · Shift 1
A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the particle is $x = \frac{A}{2}$ and it moves along positive x-axis. The displacement of particle in time t is $x = A sin (ω t + δ)$ , then the value of $δ$ will be
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: D
Q432023 · 10 Apr 2023 · Shift 1
1. A.(A), (C) and (D) only
2. B.(A) and (E) only
3. C.(A), (C) and (E) only
4. D.(B) and (E) only
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Answer: B
Q492023 · 10 Apr 2023 · Shift 1
A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity
1. A. $v$
2. B. $\frac{v}{3}$
3. C. $\frac{v}{4}$
4. D. $\frac{v}{2}$
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Answer: B
Q312023 · 10 Apr 2023 · Shift 2
A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $v$ , then the relation between $v, v_{1}$ and $v_{2}$ will be.
1. A. $V = V_{1} + V_{2}$
2. B. $V = \frac{v _{1} + V _{2}}{2}$
3. C. $\frac{1}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$
4. D. $\frac{2}{V} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$
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Answer: D
Q372023 · 10 Apr 2023 · Shift 2
Two projectiles are projected at $3 0^{\circ}$ and $6 0^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
1. A. $1 : 3$
2. B. $3 : 1$
3. C. $1 : 3$
4. D. $2 : 3$
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Answer: C
Q422023 · 8 Apr 2023 · Shift 1
Two projectiles A and B are thrown with initial velocities of $40 m/s$ and $60 m/s$ at angles $3 0^{\circ}$ and $6 0^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $(g = 10 m/s^{2})$
1. A. $4 : 9$
2. B. $2 : 3$
3. C. $3 : 2$
4. D. $1 : 1$
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Answer: A
Q492023 · 8 Apr 2023 · Shift 1
The engine of a train moving with speed $10 ms^{- 1}$ towards a platform sounds a whistle at frequency $400 Hz$ . The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in $air = 330 ms^{- 1}$ )
1. A. $200 Hz$
2. B. $412 Hz$
3. C. $400 Hz$
4. D. $388 Hz$
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Answer: C
Q442023 · 8 Apr 2023 · Shift 2
The trajectory of projectile, projected from the ground is given by $y = x - \frac{x ^{2}}{20}$ . Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.
1. A. $10 m$
2. B. $5 m$
3. C. $200 m$
4. D. $102 m$
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Answer: B
Q572023 · 8 Apr 2023 · Shift 2· Numerical answer
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Answer: 75
Q312023 · 6 Apr 2023 · Shift 1
A particle is moving with constant speed in a circular path. When the particle turns by an angle $9 0^{\circ}$ , the ratio of instantaneous velocity to its average velocity is $π : x 2$ . The value of $x$ will be -
1. A.1
2. B.7
3. C.5
4. D.2
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Answer: D
Q372023 · 6 Apr 2023 · Shift 1
A small block of mass $100 g$ is tied to a spring of spring constant $7.5 N/m$ and length $20 cm$ . The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 rad/s$ about point A, then tension in the spring is -
1. A. $0.50 N$
2. B. $1.5 N$
3. C. $0.75 N$
4. D. $0.25 N$
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Answer: C
Q562023 · 6 Apr 2023 · Shift 1· Numerical answer
A particle of mass $10 g$ moves in a straight line with retardation $2 x$ , where $x$ is the displacement in SI units. Its loss of kinetic energy for above displacement is $(\frac{10}{x})^{- n} J$ . The value of n will be ________
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Answer: 2
Q402023 · 6 Apr 2023 · Shift 2
1. A. $π m/s$
2. B. $1.5 3 m/s$
3. C. $3 m/s$
4. D. $23 m/s$
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Answer: B
Q392023 · 1 Feb 2023 · Shift 1
1. A. $\frac{v _{1} v _{2} v _{3}}{3 ( v _{1} v _{2} + v _{2} v _{3} + v _{3} v _{1} )}$
2. B. $\frac{( v _{1} + v _{2} + v _{3} )}{3}$
3. C. $\frac{( v _{1} + v _{2} + v _{3} )}{3 v _{1} v _{2} v _{3}}$
4. D. $\frac{3 v _{1} v _{2} v _{3}}{( v _{1} v _{2} + v _{2} v _{3} + v _{3} v _{1} )}$
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Answer: D
Q552023 · 1 Feb 2023 · Shift 1· Numerical answer
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 $5 \hat{i} + 2 \hat{j} + 7 \hat{k} N$ . The value of work done will be ________ $J$ .
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Answer: 40