Kinematics PYQs Set 11 (PDF)

Set 11 of 12 · Questions 301-330 of 359

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Mere Teacher · Previous Year Questions NEET Physics · Kinematics · Set 11 (Q301-330)
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301. $Two cars, at a certain instant, are 50 km apart on a line running from south to north. The one farther north is moving west at 25 km / hr . The other is moving towards north at 25 km / hr . How long do they take to reach their distance of closest approach?$ (1) $30 min$ (2) $60 min$ (3) $85 min$ (4) $90 min$ 302. $A particle moves so that its position vector is given by r = cos ω t x^+ sin ω t y^. Where ω is a constant. Which of the following is true?$ (1) $Velocity is perpendicular to r and acceleration is directed away from the origin.$ (2) $Velocity and acceleration both are perpendicular to r .$ (3) $Velocity and acceleration both are parallel to r .$ (4) $Velocity is perpendicular to r and acceleration is directed towards the origin.$ 303. $A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m s^{- 2}, the velocity with which it hits the ground is$ (1) $10.0 m / s$ (2) $20.0 m / s$ (3) $40.0 m / s$ (4) $5.0 m / s$ 304. $A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?$ (1) (2) (3) (4) 305. $The position x of a particle varies with time, (t) as x = a t^{2} - b t^{3} . The acceleration will be zero at time t is equal to$ (1) $\frac{a}{3 b}$ (2) $zero$ (3) $\frac{2 a}{3 b}$ (4) $\frac{a}{b} .$ 306. $A person aiming to reach exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m / s at an angle of 12 0^{0} with the direction of flow of water. The speed of water in the stream, is$ (1) $0.25 m / s$ (2) $0.5 m / s$ (3) $1.0 m / s$ (4) $0.433 m / s$ 307. $The velocity of a particle having magnitude of 10 ms^{- 1} in the direction of 60^{\circ} with positive X -axis is$ (1) $5 i - 53 j$ (2) $53 i - 5 j$ (3) $5 3 i + 5 j$ (4) $5 i + 53 j$ 308. $A projectile is fired from the surface of the earth with a velocity of 5 m s^{- 1} and angle 6 with the horizontal. Another projectile fired from another planet with a velocity of 3 m s^{- 1} at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^{- 2}) is (Given g = 9.8 m s^{- 2})$ (1) $3.5$ (2) $5.9$ (3) $16.3$ (4) $110.8$ 309. $An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile. The correct applied force vs distance graph will be:$ (1) (2) (3) (4) 310. $A particle moves a distance x in time t according to equation x = (t + 5)^{- 1} . The acceleration of particle is proportional to$ (1) $(velocity)^{\frac{3}{2}}$ (2) $(distance)^{2}$ (3) $(distance)^{- 2}$ (4) $(velocity)^{2/3}$ 311. $A particle of mass m is projected with velocity v making an angle of 4 5^{o} with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be$ (1) $m v 2$ (2) $zero$ (3) $2 m v$ (4) $m v / 2$ 312. $A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :$ (1) $Zero$ (2) $\frac{E}{2}$ (3) $\frac{E}{4}$ (4) $E$ 313. $A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given cos135° = -0.7)$ (1) $42 m$ (2) $47 m$ (3) $19m$ (4) $40m$ 314. $A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t_{1} and t_{2} respectively. Then the velocity of projection is (g is acceleration due to gravity)$ (1) $\frac{g t _{1} t _{2}}{2}$ (2) $\frac{g ( t _{1} + t _{2} )}{2}$ (3) $g t_{1} t_{2}$ (4) $\frac{g t _{1} t _{2}}{t _{1} + t _{2}}$ 315. $A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (g = 10 m / s^{2})$ (1) $60 m$ (2) $45 m$ (3) $80 m$ (4) $50 m .$ 316. $The distance travelled by an object in time t is given by s =(2.5) t^{2} . The instantaneous speed of the object at t = 5 s will be :$ (1) $25 m s^{- 1}$ (2) $5 m s^{- 1}$ (3) $62. 5 m s^{- 1}$ (4) $12. 5 m s^{- 1}$ 317. $The relation between time t and distance x for a moving body is given as t = m x^{2} + n x, where m land n are constants. The retardation of the motion$ (1) $2 m v^{3}$ (2) $2 mn v^{3}$ (3) $2 n v^{3}$ (4) $2 n^{2} v^{3}$ 318. $A car accelerates from rest at a constant rate α for some time after which it decelerates at a constant rate β to come to rest. If the total timeelapsed is t seconds, the total distance travelledis:$ (1) $\frac{4 αβ}{( α + β )} t^{2}$ (2) $\frac{2 αβ}{( α + β )} t^{2}$ (3) $\frac{αβ}{2 ( α + β )} t^{2}$ (4) $\frac{αβ}{4 ( α + β )} t^{2}$ 319. $A car moves a distance of 200 m . It covers the first half of the distance at speed 40 k m / h and the second half of distance at speed v . The average speed is 48 k m / h . The value of v is$ (1) $56 k m / h$ (2) $60 k m / h$ (3) $50 k m / h$ (4) $48 k m / h .$ 320. $A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to: v(x) = b x^{-2 n} where b and n are constants and x is the position of the particle. The acceleration of the particle as function of x, is given by:$ (1) $- 2 n b^{2} x^{-4 n -1}$ (2) $- 2 b^{2} x^{-2 n + 1}$ (3) $- 2 n b^{2} e^{-4 n + 1}$ (4) $- 2 n b^{2} x^{-2 n -1}$ 321. $The velocity - time graph for two bodies A and B are shown. Then the acceleration of A and B are in the ratio$ (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) $sin 25^{\circ} to sin 50^{\circ}$ 322. $In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed ’ v^{’} more than of car B . Both the cars start from rest a travel with constant acceleration a_{1} and a_{2} respectively. Then ’ v^{’} is equal to:$ (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) $\frac{a _{1} + a _{2}}{2} t$ 323. $A projectile a launched with an initial speed of 40 m / s at an angle 30^{\circ} above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile was launched to where it hits the target is (Take g = 10 m / s^{2})$ (1) $203 m$ (2) $302 m$ (3) $40 m$ (4) $2013 m$ 324. $As shown in the figure, a particle is moving with constant speed π m s^{- 1} . Considering its motion from A to B, the magnitude of the average velocity is:$ (1) $3 ms^{- 1}$ (2) $π m s^{- 1}$ (3) $1.5 3 ms^{- 1}$ (4) $23 ms^{- 1}$ 325. $Equation of a projectile is given by y = P x - Q x^{2}, where P and Q are constants. The ratio of maximum height to the range of the projectile is$ (1) $\frac{Q ^{2}}{2 P}$ (2) $\frac{P ^{2}}{Q}$ (3) $4 P$ (4) $\frac{P}{4}$ 326. $The trajectory of a projectile near the surface of the earth is given as y = 2 x - 9 x^{2} . If it were launched at an angle θ_{0} with speed v_{0} then (g = 10 ms^{- 2}) :$ (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) $θ0= sin^{- 1} 25 and v_{0} = \frac{3}{5} ms^{- 1}$ 327. $A projectile thrown from the ground has initial speed ' u' and its direction makes an angle ' θ' with the horizontal. If at maximum height from ground, the speed of projectile is half its initial speed of projection, then the maximum height reached by the projectile is [g = acceleration due to gravity, sin 30^{\circ} = cos 60^{\circ} = 0.5, cos 30^{\circ} = sin 60^{\circ} = 3 /2]$ (1) $\frac{u ^{2}}{g}$ (2) $\frac{u ^{4}}{2 g}$ (3) $\frac{2 u ^{2}}{g}$ (4) $\frac{3 u ^{2}}{8 g}$ 328. $Statement (I) : An object subjected to velocities v_{1} and v_{2} has a resultant velocity with magnitude \| v \| = (v_{1}) + (v_{2}) . Statement (II) : The magnitude of displacement is either less or equal to the path length of an object between two points. Statement (III) : The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero. Which of the following is correct?$ (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) $Statements I, II, III are false$ 329. $The trajectory of a projectile is$ (1) $semicircle$ (2) $an ellipse$ (3) $a parabola always$ (4) $a parabola in the absence of air resistance.$ 330. $A particle starts moving from time t = 0 and its coordinate is given as x (t) = 4 t^{3} - 3 t (A) The particle returns to its original position (origin) 0.866 units later(B) The particle is 1 unit away from origin at its turning point(C) Acceleration of the particle is non-negative(D) The particle is 0.5 units away from origin at its turning point(E) Particle never turns back as acceleration is non-negative Choose the correct answer from the options given below :$ (1) $A, B, C Only$ (2) $C, E Only$ (3) $A, C Only$ (4) $A, C, D Only$