Practice Questions

Q3. A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre: (1) 8 cm (2) 4 cm (3) 1 cm (4) 2 cm

Q3. A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 m s – 1 . Neglecting the air resistance, the speed with which the stone hits the ground will be _____ m s – 1 (given, 𝑔 = 10 m s – 2 ). (1) 20 (2) 15 (3) 30 (4) 25

Q3. A stone is projected at angle 30° to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be : (1) 1 : 2 (2) 1 : 4 (3) 4 : 1 (4) 4 : 3

Q3. A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3. 14 s. The radius of the merry- go-round is 2 m. The centrifugal force on the child will be (1) 80 N (2) 40 N (3) 100 N (4) 50 N

Q3. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be : (1) 2√gR (2) √gR (3) √gR2 (4) √2gR

Q4. Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity ( 𝑔) . Statement II : The effect of rotation of the earth on the value of 𝑔 at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below (1) Statement I is false but statement II is true (2) Both Statement I and Statement II are true (3) Both Statement I and Statement II are false (4) Statement I is true but statement II is false

Q4. A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0 ) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0. 25 J . The spring constant of the spring is ______ N m−1 .

Q4. A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is 2 ) s . The value of t is ______. moving with an initial speed of 54 km h−1 is t(1–e– π

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. Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below (1) Statement I is correct but statement II is incorrect (2) Statement I is incorrect but statement II is correct (3) Both statement I and Statement II are correct (4) Both statement I and statement II are incorrect

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. 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 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 stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936 x m s−2 . The value of x ______. [Take π = 227 ]

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. 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 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. Given below are two statements: Statement-I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement-II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below: (1) Both Statement I and Statement II are false (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are true (4) Statement I is false but Statement II is true

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

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 body of mass 200 g is tied to a spring of spring constant 12. 5 N m−1 , while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad s−1 , then the ratio of extension in the spring to its natural length will be : (1) 1 : 2 (2) 1 : 1 (3) 2 : 3 (4) 2 : 5 Q5. → + N , where ˆi A body of mass 1 kg begins to move under the action of a time dependent force F = (tˆi 3t2ˆj) and ˆj are the unit vectors along x and y axis. The power developed by above force, at the time t = 2 s , will be _______ W.

Q4. Two bodies are projected from ground with same speeds 40 m s−1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m. (Given g = 10 m s−2 )

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. Two projectiles A and B are thrown with initial velocities of 40 m s−1 and 60 m s−1 at angles 30° and 60° with the horizontal respectively. The ratio of their ranges respectively is (g = 10 m s−2) (1) 4 : 9 (2) 2 : √3 (3) √3 : 2 (4) 1 : 1 m s−1 . If the force acting on the

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