Kinematics PYQs Set 9 (PDF)

Set 9 of 14 · Questions 241-270 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 9 (Q241-270)
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241. $Two particles A and B are connected by arigid rod A B . The rod slides along perpendicular rails as shown here. Th e velocity of A to the left \leftarrow A is 10 m / s . What is the velocity of B when angle α = 6 0^{o} ?$ (1) $10 m / s$ (2) $9.8 m / s$ (3) $5.8 m / s$ (4) $17.3 m / s .$ 242. $A car covers the first half of the distance between two places at 40 k m / h and another half at 60 k m / h . The average speed of the car is$ (1) $40 k m / h$ (2) $48 k m / h$ (3) $50 k m / h$ (4) $60 k m / h .$ 243. $An object is projected with kinetic energy K from a point A at an angle 60^{\circ} with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is:$ (1) $1 : 4$ (2) $2 : 3$ (3) $3 : 4$ (4) $1 : 2$ 244. $The angle of projection of a particle is measured from the vertical axis as φ and the maximum height reached by the particle is h_{m} . Here h_{m} as function of φ can be presented as$ (1) (2) (3) (4) 245. $A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is$ (1) $g/2n$ (2) $g/n$ (3) $2gn$ (4) $g/ 2 n^{2}$ 246. $Two bodies were thrown simultaneously from the origin, one straight up and the other, at angle 60^{\circ} to the vertical. The initial velocity of each body is equal to 10 ms^{- 1} . Neglecting the air resistance, the distance between the two bodies after t = 2 s is (Take, g = 10 m / s^{2})$ (1) $20 m$ (2) $202 m$ (3) $53 m$ (4) $30 m$ 247. $A projectile is projected at 10 m s^{- 1} by making at an angle 60^{\circ} to the horizontal. After some time its velocity makes an angle of 30^{\circ} to the horizontal. Its speed at this instant (in m s^{- 1}) is$ (1) $\frac{10}{3}$ (2) $103$ (3) $\frac{5}{3}$ (4) $53$ 248. $Starting from the origin at time t = 0, with initial velocity 5 j^ms^{- 1} a particle moves in the x - y plane with a constant acceleration of (10 i^+ 4 j^) ms^{- 2} . At time t, its coordinates are (20 m, y_{0} m) . The values of t and y_{0} are, respectively$ (1) $4 s and 52 m$ (2) $2s and 24 m$ (3) $5 s and 25 m$ (4) $2s and 18 m$ 249. $Consider the following vectors. Choose the correct statement.$ (1) $E = A - B and A = D + C$ (2) $- E = - A + B and A = - D + C$ (3) $E=-A-B and E = - B + D + C$ (4) $E=-A-B and E = - B + C - D$ 250. $A car travels a distance of 'x' with speed V_{1} and then same distance ‘x’ with speed V_{2} in the same direction. The average speed of the car is:$ (1) $\frac{v _{1} v _{2}}{2 ( v _{1} + v _{2} )}$ (2) $\frac{v _{1} + v _{2}}{2}$ (3) $\frac{2 x}{v _{1} + v _{2}}$ (4) $\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}$ 251. $A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is$ (1) $2R$ (2) $R = (π^{2} + 4)$ (3) $R = (π^{2} + 1)$ (4) $2 R = (1 + 4 π^{2})$ 252. $If the velocity of a particle is v = A t + B t^{2}, where A and B are constants, then the distance travelled by it between 1 s and 2 s is$ (1) $\frac{3}{2} A + \frac{7}{3} B$ (2) $\frac{A}{2} + \frac{B}{3}$ (3) $\frac{3}{2} A + 4 B$ (4) $3 A + 7 B$ 253. $A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is$ (1) $0,1$ (2) $\frac{π + 4}{2}, 0$ (3) $21.4, \frac{π + 4}{2}$ (4) $0, 21.4$ 254. $A person is standing in an elevator. In which situation, he experiences weight loss ?$ (1) $When the elevator moves upward with constant acceleration$ (2) $When the elevator moves downward with constant acceleration$ (3) $When the elevator moves upward with uniform velocity$ (4) $When the elevator moves downward with uniform velocity$ 255. $Motion of a particle in x-y plane is described by a set of following equations x = 4 cos (ω t) m and y = 4 sin (ω t) m. The path of particle will be -$ (1) $circular$ (2) $helical$ (3) $parabolic$ (4) $elliptical$ 256. $A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 k m / h and 40 k m / h respectively the velocity of the car midway between P and Q is$ (1) $33.3 k m / h$ (2) $202 km/h$ (3) $252 km/h$ (4) $35 k m / h .$ 257. $The position x of a particle with respect to time t along x ‐axis is given by x = 9 t^{2} - t^{3} where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction?$ (1) $54 m$ (2) $81 m$ (3) $24 m$ (4) $32 m$ 258. $A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given g = 9.8 m/ s^{2})$ (1) $5m$ (2) $10m$ (3) $19.8m$ (4) $24.5m$ 259. $The stream of a river is flowing with a speed of 2 km / h . A swimmer can swim at a speed of 4 km / h . What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?$ (1) $90^{\circ}$ (2) $150^{\circ}$ (3) $120^{\circ}$ (4) $60^{\circ}$ 260. $If the maximum height and range of a projectile are 3 m and 4 m respectively, then the velocity of the projectile is (Take, g = 10 ms^{- 2})$ (1) $20 \frac{6}{5} ms^{- 1}$ (2) $10 \frac{3}{2} ms^{- 1}$ (3) $10 \frac{2}{3} ms^{- 1}$ (4) $20 \frac{5}{6} ms^{- 1}$ 261. $A particle is projected from the ground with some initial velocity making an angle of 45^{\circ} with the horizontal. If it reaches a height of 7.5 m above the ground, while it travels a horizontal distance of 10 m from the point of projection, then the initial speed of particle is (assume, g = 10 m / s^{2})$ (1) $10 m / s$ (2) $20 m / s$ (3) $15 m / s$ (4) $25 m / s$ 262. $The displacement-time graph of two moving particles makes angles of 30^{\circ} and 45^{\circ} with the X -axis as shown in the figure. The ratio of their respective velocity is [NEET 2022]$ (1) $1 : 1$ (2) $1 : 2$ (3) $1 : 3$ (4) $3 : 1$ 263. $A small object is thrown at an angle 45^{\circ} to the horizontal with an initial velocity v_{0} . The velocity is averaged for first 2 s and the magnitude of average velocity comes out to be same as that of initial velocity, i.e. (v_{0}) . The magnitude (v_{0}) will be (take, g = 10 m / s^{2})$ (1) $3 m / s$ (2) $32 m / s$ (3) $4 m / s$ (4) $5 m / s$ 264. $A car driver is trying to jump across a path as shown in figure by driving horizontally off a cliff X at the speed 10 m / s . When he touches peak Z (ignore air resistance). What would be speed? (Use, g = 10 m / s^{2})$ (1) $30 m / s$ (2) $40 m / s$ (3) $15 m / s$ (4) $50 m / s$ 265. $A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 3 0^{0} with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the line AB should be^{0}, so that the swimmer reaches point B.$ 266. $A particle is projected at an angle of 30^{\circ} from horizontal at a speed of 60 m / s . The height traversed by the particle in the first second is h_{0} and height traversed in the last second, before it reaches the maximum height, is h_{1} . The ratio h_{0} : h_{1} is [Take, g = 10 m / s^{2}]$ 267. $A car covers AB distance with first one-third at velocity v_{1} m s^{- 1}, second one-third at v_{2} m s^{- 1} and last one-third at v_{3} m s^{- 1} . If v_{3} = 3 v_{1}, v_{2} = 2 v_{1} and v_{1} = 11 m s^{- 1} then the average velocity of the car is ________m s^{- 1} .$ 268. $A projectile fired at 30° to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is m s"^{1} . (Given g = 10 m s^{- 2})$ 269. $A particle is moving with constant acceleration 'a'. Following graph shows υ^{2} versus x (displacement) plot. The acceleration of the particle is ..... m/ s^{2} .$ 270. $A small block slides down from the top of hemisphere of radius R=3m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is m. (Assume there is no friction between the block and the hemisphere)$