A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ `m_o` of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes :- `m=(m_0)/((1-v^2)^(1/2))` Guess where to put the missing c.

A mass of 2 kg is attached to the spring of spring constant 50 N m^-1 . The lock is pulled to a distance of 5 cm from its equilibrium position at x = 0 on a horizontal frictionless surface from rest at t = 0. Write the expression for tis displacement at anytime t.

Check the correctness of the physical relation: v= sqrt((2GM)/(R)) , where v is velocity, G is gavitational constant, M is mass and R is radius of the earth.

The question given below consist of an assertion (A) and a reason ( R). Use the following key to choose the appropriate answer to these questions from the codes (a), (b), ( c) and (d) given below: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is NOT the correct explanation of A. (c) A is true but R is false. (d) A is false and R is also false Assertion: In a nuclear process mass gets converted into energy. Reason: According to Einstein's mass energy equivalence relation, mass m is equivalent to energy E, given be the relation E=mc^2 where c is the speed of light in vacuum.

A ball of mass m, moving with a speed 2v_0 collides inelastically (e>0) with an identical ball at rest. Show that for head-on collision, both the balls move forward.

An elevator of total mass (elevator+ passenger) 3600 kg in moving up with a constant speed of 2 ms^-1 . A frictional force of 1300 M opposes its motion. Determine the minimum power delivered by the motor to the elevator.

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?

A small piece of mass m moves in such a way the P.E. = -(1)/(2)mkr^(2) . Where k is a constant and r is the distance of the particle from origin. Assuming Bohr's model of quantization of angular momentum and circular orbit, r is directly proportional to :