Practice Questions

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. 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 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 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. 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. 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. 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 particle of mass 100 g is projected at time t = 0 with a speed 20 m s–1 at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m2 s−1 . The value of K is ______. (Take g = 10 m s−2 )

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. 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. To maintain a speed of 80 km h−1 by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0. 04 ]

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. An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2 N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx , where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = nk sin θ . The value of n is ______.

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. 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. 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 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. 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 body of mass 5 kg is moving with a momentum of 10 kg m s−1 . Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _____ J.

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. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth 𝑅𝑒= 6400 km) (1) 9 . 8 N (2) 4 . 9 N (3) 19 . 6 N (4) 8 N

Q5. A body is dropped on ground from a height h1 and after hitting the ground, it rebounds to a height h2 . If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy of the body is x . The value of x is _____. 4

Q5. The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given 𝑔= 𝜋2 m s-2, 𝑅= radius of earth) (1) √2R (2) √8R (3) √32R (4) √4R

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