Practice Questions

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 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. 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. 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 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 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. 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 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. 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. 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. 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 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. 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. 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. 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. 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. 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

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. A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30° with horizontal with an effective acceleration of 1 m s−2 . The power delivered by the puling force at t = 10 s from the start is _____ W. [Use g = 10 m s−2 ] (Calculate the nearest integer value)

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 nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2 . The ratio of their 1 nuclear sizes will be ( x3 ) 3 . The value of ‘ x’ is:

Q5. A force F = (5 + 3y2) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is ______ J .

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