Kinematics PYQs Set 13 (PDF)

Set 13 of 14 · Questions 361-390 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 13 (Q361-390)
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361. $The velocity - time graph for two bodies A and B are shown. Then the acceleration of A and B are in the ratio$ (1) $tan 25^{\circ} to tan 50^{\circ}$ (2) $cos 25^{\circ} to cos 50^{\circ}$ (3) $tan 25^{\circ} to tan 40^{\circ}$ (4) $sin 25^{\circ} to sin 50^{\circ}$ 362. $In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed ’ v^{’} more than of car B . Both the cars start from rest a travel with constant acceleration a_{1} and a_{2} respectively. Then ’ v^{’} is equal to:$ (1) $\frac{2 a _{1} a _{2}}{a _{1} + a _{2}} t$ (2) $2 a_{1} a_{2} t$ (3) $a_{1} a_{2} t$ (4) $\frac{a _{1} + a _{2}}{2} t$ 363. $A projectile a launched with an initial speed of 40 m / s at an angle 30^{\circ} above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile was launched to where it hits the target is (Take g = 10 m / s^{2})$ (1) $203 m$ (2) $302 m$ (3) $40 m$ (4) $2013 m$ 364. $As shown in the figure, a particle is moving with constant speed π m s^{- 1} . Considering its motion from A to B, the magnitude of the average velocity is:$ (1) $3 ms^{- 1}$ (2) $π m s^{- 1}$ (3) $1.5 3 ms^{- 1}$ (4) $23 ms^{- 1}$ 365. $Equation of a projectile is given by y = P x - Q x^{2}, where P and Q are constants. The ratio of maximum height to the range of the projectile is$ (1) $\frac{Q ^{2}}{2 P}$ (2) $\frac{P ^{2}}{Q}$ (3) $4 P$ (4) $\frac{P}{4}$ 366. $The trajectory of a projectile near the surface of the earth is given as y = 2 x - 9 x^{2} . If it were launched at an angle θ_{0} with speed v_{0} then (g = 10 ms^{- 2}) :$ (1) $θ0= sin^{- 1} 15 and v_{0} = \frac{5}{3} ms^{- 1}$ (2) $θ0= cos^{- 1} 25 and v_{0} = \frac{3}{5} ms^{- 1}$ (3) $θ_{0} = cos^{- 1} \frac{1}{5} and v_{0} = \frac{5}{3} m s^{- 1}$ (4) $θ0= sin^{- 1} 25 and v_{0} = \frac{3}{5} ms^{- 1}$ 367. $A projectile thrown from the ground has initial speed ' u' and its direction makes an angle ' θ' with the horizontal. If at maximum height from ground, the speed of projectile is half its initial speed of projection, then the maximum height reached by the projectile is [g = acceleration due to gravity, sin 30^{\circ} = cos 60^{\circ} = 0.5, cos 30^{\circ} = sin 60^{\circ} = 3 /2]$ (1) $\frac{u ^{2}}{g}$ (2) $\frac{u ^{4}}{2 g}$ (3) $\frac{2 u ^{2}}{g}$ (4) $\frac{3 u ^{2}}{8 g}$ 368. $Statement (I) : An object subjected to velocities v_{1} and v_{2} has a resultant velocity with magnitude \| v \| = (v_{1}) + (v_{2}) . Statement (II) : The magnitude of displacement is either less or equal to the path length of an object between two points. Statement (III) : The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero. Which of the following is correct?$ (1) $Statements I, II, III are true$ (2) $Statements I, II are true, but Statement III is false$ (3) $Statements II, III are true, but Statement I is false$ (4) $Statements I, II, III are false$ 369. $The trajectory of a projectile is$ (1) $semicircle$ (2) $an ellipse$ (3) $a parabola always$ (4) $a parabola in the absence of air resistance.$ 370. $A particle starts moving from time t = 0 and its coordinate is given as x (t) = 4 t^{3} - 3 t (A) The particle returns to its original position (origin) 0.866 units later(B) The particle is 1 unit away from origin at its turning point(C) Acceleration of the particle is non-negative(D) The particle is 0.5 units away from origin at its turning point(E) Particle never turns back as acceleration is non-negative Choose the correct answer from the options given below :$ (1) $A, B, C Only$ (2) $C, E Only$ (3) $A, C Only$ (4) $A, C, D Only$ 371. $Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x_{P} (t) = a t + b t^{2} and x_{Q} (t) = f t - t^{2} . At what time do the cars have the same velocity?$ (1) $\frac{a - f}{1 + b}$ (2) $\frac{a + f}{2 _{(} b - 1 _{)}}$ (3) $\frac{a + f}{2 ( 1 + b )}$ (4) $\frac{f - a}{2 ( 1 + b )}$ 372. $A particle moves along a straight line such that its displacement at any time t is given by s = (t^{3} - 6 t^{2} + 3 t + 4) metres. The velocity when the acceleration is zero is$ (1) $3 m/s$ (2) $42 m/s$ (3) $- 9 m/s$ (4) $- 15 m/s$ 373. $A car moves from X to Y with a uniform speed v_{u} and returns to Y with a uniform speed v_{d} . The average speed for this round trip is$ (1) $v_{u} v_{d}$ (2) $\frac{v _{u} v _{d}}{v _{d} + v _{u}}$ (3) $\frac{v _{u} + v _{d}}{2}$ (4) $\frac{2 v _{u} v _{d}}{v _{d} + v _{u}}$ 374. $A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by x_{1} (t) after time ‘t’ and that of second body by x_{2} (t) after the same time interval. Which of the following graphs correctly describes (x_{1} - x_{2}) as a function of time ‘t’ ?$ (1) (2) (3) (4) 375. $The distance travelled by a particle is related to time t as x = 4 t^{2} . The velocity of the particle at t =5s is.$ (1) $40 m s^{- 1}$ (2) $25 m s^{- 1}$ (3) $20 m s^{- 1}$ (4) $8 m s^{- 1}$ 376. $A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform dielectric field E. Due to the force qE. Its velocity increases from 0 to 6 m / s in one second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 second are respectively. [NEET 2018]$ (1) $1 m / s, 3.5 m / s$ (2) $1 m / s, 3 m / s$ (3) $2 m / s, 4 m / s$ (4) $1.5 m / s, 3 m / s$ 377. $A man (mass = 50 Kg) and his son (mass = 20 Kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms^{- 1} with respect to the man. The speed of the man with respect to the surface is:$ (1) $0.28 ms^{- 1}$ (2) $0.20 ms^{- 1}$ (3) $0.47 ms^{- 1}$ (4) $0.14 ms^{- 1}$ 378. $An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?$ (1) $Momentum$ (2) $Potential energy$ (3) $Acceleration$ (4) $Force$ 379. $A particle shows distance - time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point$ (1) $D$ (2) $A$ (3) $B$ (4) $C$ 380. $A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S . The displacement of a cyclist is:$ (1) $8 km$ (2) $8 km$ (3) $6 km$ (4) $4 km$ 381. $A projectile is fired from the surface of the earth with a velocity of 5 m s^{-1} and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^{-1} at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is : (given = 9.8 m s^{-2})$ (1) $3.5$ (2) $5.9$ (3) $16.3$ (4) $110.8$ 382. $A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F_{0} [1 - (\frac{t - T}{T})^{2}] Where F_{0} and T are constants. The force acts only for the time interval 2T. The velocity of the particle after time 2T is :$ (1) $2 F_{0} T/M$ (2) $F_{0} T/2M$ (3) $4 F_{0} T/3M$ (4) $F_{0} T/3M$ 383. $One end of string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’ the net force on the particle (directed towards center) will be (T represents the tension in the string)$ (1) $T$ (2) $T + \frac{m ν ^{2}}{ℓ}$ (3) $T - \frac{m ν ^{2}}{ℓ}$ (4) $zero$ 384. $Two boys are standing at the ends A and B of a ground where A B = a . The boy a B starts running in a direction perpendicular to A B with velocity v_{1} . The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is$ (1) $\frac{a}{v ^{2} + v _{1^{2}}}$ (2) $\frac{a}{v + v _{1}}$ (3) $\frac{a}{v - v _{1}}$ (4) $\frac{a}{v ^{2} - v _{1}^{2}}$ 385. $A ball is released from a height h. If t_{1} and t_{2} be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t_{1} and t_{2} .$ (1) $t_{1} = (2) t_{2}$ (2) $t_{1} = (2 - 1) t_{2}$ (3) $t_{2} = (2 + 1) t_{1}$ (4) $t_{2} = (2 - 1) t_{1}$ 386. $Two bodies A (of mass 1 k g) and B (of mass 3 k g) are dropped from heights of 16 m and 25 m, respectively the ratio of the time taken by them to reach the ground is$ (1) $4/5$ (2) $5/4$ (3) $12/5$ (4) $5/12$ 387. $A rocket is moving in a gravity free space with a constant acceleration of 2 m s^{-2} along +x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0. 3 m s^{1} relative to the rocket. At the same time, another ball is thrown in -x direction with a speed of 0. 2 m s^{-1} from its right end relative to the rocket. The time in seconds when the two balls hit each other is$ 388. $A particle is moving in a straight line such that its velocity is increasing at 5 m s^{- 1} per meter.The acceleration of the particle is_____m s^{- 2} at a point where its velocity is 20 m s^{- 1} .$ 389. $A person is swimming with a speed of 10 m / s at an angle of 120^{\circ} with the flow and reaches to a pointdirectly opposite on the other side of the river. The speed of the flow is ’ x ’ m / s . The value of ’ x ’ to the nearestinteger is____$ 390. $A body is projected from the ground at an angle of 45° with the horizontal. Its velocity after 2s is 20 m s^{- 1} . The maximum height reached by the body during its motion is\dots\dotsm. (use g = 10 m s^{- 1})$