Kinematics PYQs Set 5 (PDF)

Set 5 of 14 · Questions 121-150 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 5 (Q121-150)
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121. $A body starts from rest with uniform acceleration. If its velocity after n^{th} second (last second) is ' V' then its displacement in the last two seconds is$ (1) $\frac{2 V ( n + 1 )}{n}$ (2) $\frac{V ( n + 1 )}{n}$ (3) $\frac{V ( n - 1 )}{n}$ (4) $\frac{2 V ( n - 1 )}{n}$ 122. $When a particle moved from point A (2, 2, 3) to point B (6, 6, 9), its displacement vector is$ (1) $4 i + 4 j + 6 k$ (2) $8 i + 8 j + 12 k$ (3) $4 i + 8 j + 6 k$ (4) $8 i + 4 j + 6 k$ 123. $Two projectiles are fired with same initial speed from same point on ground at angles of (45^{\circ} - α) and (45^{\circ} + α), respectively, with the horizontal direction. The ratio of their maximum heights attained is :$ (1) $\frac{1 - tan α}{1 + tan α}$ (2) $\frac{1 - sin 2 α}{1 + sin 2 α}$ (3) $\frac{1 + sin 2 α}{1 - sin 2 α}$ (4) $\frac{1 + sin α}{1 - sin α}$ 124. $If the velocity of a particle is v = At + B t^{2}, where A and B are constants, then the distance travelled by it between 1 s and 2 s is [NEET 2016]$ (1) $3 A + 7 B$ (2) $\frac{3}{2} A + \frac{7}{3} B$ (3) $\frac{A}{2} + \frac{B}{3}$ (4) $\frac{3}{2} A + \frac{4}{3} B$ 125. $A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 ms^{- 1} . The ball strikes the water surface after 4 s. The height of bridge above water surface is (take, g = 10 ms^{- 2}). [NEET 2023]$ (1) $60 m$ (2) $64 m$ (3) $68 m$ (4) $56 m$ 126. $A helicopter rises from rest on the ground vertically upwards with a constant acceleration g . A food packet is dropped from the helicopter when it is at a height h . The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]$ (1) $t = 3.4 (\frac{h}{g})$ (2) $t = 1.8 \frac{h}{g}$ (3) $t = \frac{2 h}{3 g}$ (4) $t = \frac{2}{3} (\frac{h}{g})$ 127. $A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0. 2 rad s^{- 1} . The centripetal force acting on the vehicle is:$ (1) $560 N$ (2) $2800 N$ (3) $2240 N$ (4) $14 N$ 128. $The resultant of two vectors A and B is perpendicular to vector A and the resultant magnitude is equal to half of the magnitude of B, then the angle between A and B is$ (1) $30^{\circ}$ (2) $60^{\circ}$ (3) $150^{\circ}$ (4) $120^{\circ}$ 129. $A particle starts from the origin at t = 0 s with a velocity of 10 j m s^{- 1} and moves in the x - y plane with a constant acceleration of (8 i + 2 j) m s^{- 2} . At an instant when the x -coordinate of the particle is 16 m, y -coordinate of the particle is$ (1) $16 m$ (2) $28 m$ (3) $36 m$ (4) $24 m$ 130. $A ball is dropped from a bridge that is 45 m above the water. It falls directly into a boat which is moving with constant velocity. The boat is 12 m away from the point of impact when the ball is dropped. The speed of the boat is (take, g = 10 m / s^{2})$ (1) $2 m / s$ (2) $3 m / s$ (3) $4 m / s$ (4) $5 m / s$ 131. $Two trains A and B of length l and 4 l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h^{- 1} and 72 km h^{- 1}, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l)$ (1) $1200m$ (2) $900m$ (3) $1800m$ (4) $2700m$ 132. $A particles is performing a uniform circular motion along circle of radius ' R'. In half the period of revolution, its displacement and distance covered are respectively$ (1) $2 R, 2 πR$ (2) $R, πR$ (3) $2 R, 2 πR$ (4) $2 R, πR$ 133. $A particle is moving in a straight line. The variation of position ' x' as a function of time ' t' is given as x = (t^{3} - 6 t^{2} + 20 t + 15) m . The velocity of the body when its acceleration becomes zero is :$ (1) $4 m / s$ (2) $8 m / s$ (3) $10 m / s$ (4) $6 m / s$ 134. $A, B, C are points in a vertical line such that AB = BC . If a body falls freely from rest at A, t_{1} and t_{2} are times taken to travel distances AB and BC, then ratio (t_{2} / t_{1}) is$ (1) $2 + 1$ (2) $2 - 1$ (3) $22$ (4) $\frac{1}{2 + 1}$ 135. $A particle of mass m projected with a velocity ' u' making an angle of 30^{\circ} with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is :$ (1) $\frac{3}{16} \frac{m u ^{3}}{g}$ (2) $\frac{3}{2} \frac{m u ^{2}}{g}$ (3) $\frac{m u ^{3}}{2 g}$ (4) $zero$ 136. $A particle is projected with velocity 2 gh and at an angle 60^{\circ} to the horizontal so that it just clears two walls of equal height h which are at a distance 2 h from each other. The time taken by the particle to travel between these two walls is$ (1) $2 \frac{2 h}{g}$ (2) $\frac{h}{2 g}$ (3) $2 \frac{h}{g}$ (4) $\frac{h}{g}$ 137. $A ball is thrown vertically downward with a velocity of 20 m / s from the top of a tower. It hits the ground after some time with a velocity of 80 m / s . The height of the tower is (g = 10 m / s^{2}) [NEET 2020]$ (1) $340 m$ (2) $320 m$ (3) $300 m$ (4) $360 m$ 138. $A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π = 3.14) :$ (1) $140.5$ (2) $118.9$ (3) $139.4$ (4) $220.0$ 139. $The displacements of a particle starting from rest at t = 0 is given by s = 9 t^{2} - 2 t^{3} . The time in seconds at which the particle will attain zero velocity is$ (1) $8 s$ (2) $6 s$ (3) $4 s$ (4) $3 s$ 140. $A ball falls freely from a height h on a rigid horizontal plane. If the coefficient of restitution is e, then the total distance travelled by the ball before hitting the plane second time is$ (1) $he^{2}$ (2) $h (1 + 2 e^{2})$ (3) $h (1 - 2 e^{2})$ (4) $h (1 + e^{2})$ 141. $The co-ordinates of a particle moving in x - y plane are given by : x = 2 + 4 t, y = 3 t + 8 t^{2} . The motion of the particle is :$ (1) $uniformly accelerated having motion along a parabolic path.$ (2) $uniform motion along a straight line.$ (3) $uniformly accelerated having motion along a straight line.$ (4) $non-uniformly accelerated.$ 142. $A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \frac{n u ^{2}}{25 g}, where value of n is: (Given, ' g' is the acceleration due to gravity.)$ (1) $6$ (2) $12$ (3) $18$ (4) $24$ 143. $A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t_{1} and t_{2} are the values of the time taken by it to hit the target in two possible ways, the product t_{1} t_{2} is:$ (1) $R /4 g$ (2) $R / g$ (3) $R /2 g$ (4) $2 R / g$ 144. $A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to \frac{81}{100} of the height throughwhich it falls. Find the average speed of the ball. (Take = 10 ms^{- 2})$ (1) $3.0 ms^{- 1}$ (2) $3.50 ms^{- 1}$ (3) $2.0 ms^{- 1}$ (4) $2.50 ms^{- 1}$ 145. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: When a body is projected at an angle 45°, its range is maximum. Reason R: For maximum range, the value of sin 2 θ should be equal to one. In the light of the above statements, choose the correct answer from the options given below:$ (1) $A is false but R is true$ (2) $A is true but R is false$ (3) $Both A and R are correct and R is the correct explanation of A$ (4) $Both A and R are correct but R is NOT the correct explanation of A$ 146. $For a projectile if α is the angle of projection, R is the range, h is the maximum height, T is the time of flight then$ (1) $tan α = \frac{R}{2 h}, h = \frac{g T ^{2}}{8}$ (2) $tan α = \frac{R}{4 h}, h = \frac{g T ^{2}}{8}$ (3) $tan α = \frac{4 h}{R}, h = \frac{g T ^{2}}{8}$ (4) $tan α = \frac{4 h}{?}, h = \frac{g T ^{2}}{4}$ 147. $At time t = 0, a particle leaves the origin and moves in the positive direction of the X -axis. If the velocity of the particles varies as v (t) = v_{0} (1 - \frac{t}{t _{0}}), (v_{0}) = 10 m / s and t_{0} = 10 s then the distance covered by the particle during the first 20 s is$ (1) $200 m$ (2) $100 m$ (3) $0 m$ (4) $400 m$ 148. $A particle starts from origin at t = 0 with a velocity 5 im / s and moves in x - y plane under action of a force which produces a constant acceleration of (3 i + 2 j) m / s^{2} . If the x -coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is α m / s . The value of α is______$ 149. $The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is_____m.$ 150. $A person travelling on a straight line moves with a uniform velocity v_{1} for a distance x and with a uniform velocity v_{2} for the next \frac{3}{2} x distance. The average velocity in this motion is \frac{50}{7} m / s . If v_{1} is 5 m / s then v_{2} -_________m / s .$