Practice Questions

Q4. A body of mass (5 ± 0. 5) kg is moving with a velocity of (20 ± 0. 4) m s−1. Its kinetic energy will be (1) (1000 ± 0. 14) J (2) (500 ± 0. 14) J (3) (500 ± 140) J (4) (1000 ± 140) J

Q4. A mass 𝑚 is attached to two springs as shown in figure. The spring constants of two springs are 𝐾1 and 𝐾2 . For the frictionless surface, the time period of oscillation of mass 𝑚 is (1) 𝑚 (2) 1 K1 - K2 2𝜋√ K1 + K2 2𝜋√ 𝑚 (3) 𝑚 (4) 1 K1 + K2 2𝜋√ K1 - K2 2𝜋√ 𝑚

Q4. A car is moving with a constant speed of 20 m s−1 in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m s−2 ) (1) π (2) π 6 2 (3) π (4) π 4 3

Q4. As per the given figure, a small ball 𝑃 slides down the quadrant of a circle and hits the other ball 𝑄 of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball 𝑄 after collision will be : ( 𝑔 = 10 m s-2 ) (1) 0 (2) 0 . 25 m s-1 (3) 2 m s-1 (4) 4 m s-1

Q4. A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation v = 10√x m s−1 the force acting on the body is: (1) 125 N (2) 25 N (3) 166 N (4) 5 N

Q4. Consider a block kept on an inclined plane (inclined at 45° ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane (µ) is equal to : . (1) 0. 33 (2) 0. 60 (3) 0. 25 (4) 0. 50

Q4. 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

Q4. An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s-1 to keep it in position. The number of bullets fired per second by the machine gun is : (1) 50 (2) 25 (3) 100 (4) 5 𝜌

Q4. A small particle of mass m moves in such a way that its potential energy U = 12 mω2r2 where ω is constant and r is the distance of the particle from origin. Assuming Bohr’s quantization of momentum and circular orbit, the radius of nth orbit will be proportional to (1) √n (2) n1 (3) n2 (4) n

Q4. 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) 𝑣 (2) 𝑣 3 4 𝑣 (3) 𝑣 (4) 2

Q4. A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0. 34. [Take g = 10 m s−2 ] (1) 3. 4 m s−1 (2) 22. 4 m s−1 (3) 13 m s−1 (4) 17 m s−1

Q4. A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, 𝑔 = 10 m s – 2 ): (1) 0 . 60 (2) 0 . 75 (3) 0 . 50 (4) 0 . 25 𝑣𝑒

Q4. The position vector of a particle related to time t is given by →r= (10tˆi + 15t2ˆj + 7ˆk)m . The direction of net force experienced by the particle is : (1) Positive x-axis (2) In x −y plane (3) Positive y-axis (4) Positive z-axis

Q4. A bullet of mass 0. 1 kg moving horizontally with speed 400 m s−1 hits a wooden block of mass 3. 9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is _______. (1) 0. 90 (2) 0. 50 (3) 0. 65 (4) 0. 25

Q5. At any instant the velocity of a particle of mass 500 g is (2t ˆi + 3t2 ˆj) + x N . Then the value of x will be: particle at t = 1 s is (ˆi ˆj) (1) 3 (2) 4 (3) 2 (4) 6

Q5. A small block of mass 100 g is tied to a spring of spring constant 7 . 5 N m-1 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-1about point 𝐴, then tension in the spring is (1) 0 . 75 N (2) 0 . 25 N (3) 0 . 50 N (4) 1 . 5 N

Q5. Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is (1) √3: 1 (2) 3: 1 (3) 9: 1 (4) 1: 1

Q5. A body of mass 10 kg is moving with an initial speed of 20 m s−1 . The body stops after 5 s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity g = 10 m s−2 ) (1) 0. 2 (2) 0. 3 (3) 0. 5 (4) 0. 4

Q5. Two planets A and B of radii 𝑅 and 1 . 5 𝑅 have densities 𝜌 and 𝜌 respectively. The ratio of acceleration due to 2 gravity at the surface of B to A is: (1) 2 : 3 (2) 2 : 1 (3) 3 : 4 (4) 4 : 3

Q5. A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be: (Given g = acceleration due to gravity on the earth.) (1) √2gR (2) √gR (3) √4gR (4) √gR2

Q5. A block of √3 kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of 30° with the wall. The tension T is : (Given g = 10 m s–2 ) (1) 20 N (2) 25 N (3) 10 N (4) 15 N

Q5. At a certain depth 𝑑 below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3𝑅 above earth surface. Where 𝑅 is Radius of earth (Take 𝑅 = 6400 km). The depth 𝑑 is equal to (1) 5260 km (2) 640 km (3) 2560 km (4) 4800 km

Q5. A block of mass m slides down the plane inclined at angle 30° with an acceleration 4g . The value of coefficient of kinetic friction will be : (1) 2√3+1 (2) 1 2 2√3 (3) √3 (4) 2√3−1 2 2

Q5. If earth has a mass nine times and radius twice to the of a planet 𝑃. Then 3 √𝑥𝑚𝑠-1 will be the minimum velocity required by a rocket to pull out of gravitational force of 𝑃, where ve is escape velocity on earth. The value of 𝑥 is (1) 2 (2) 3 (3) 18 (4) 1

Q5. Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is: (1) 3 : 4 (2) 9 : 16 (3) 16 : 9 (4) 4 : 3