A body of mass m is situated in a potential field U(x) `=(U_0(1 - cosax)` when `U_0` and a are constants. Find the time period of small oscillations.

Explain the oscillation of a liquid in a U-tube. Find its time period.

A body P of mass m is thrown with velocity u at an angle 30^@ to the horizontal and another body Q is of teh same mass be projected with velocity u at an angle 60^@ to the horizontal .Find the ratio of the horizonta range nd maximum heights of P and Q.

A vibration magnetometer placed in magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 sec in earth's horizontal magnetic field of 24 microtesla. When a horizontal field of 18 microtesla is produced opposite to the earth's field by placing a current carrying wire, the new time period of magnet will be

The masses m_1 and m_2 together are suspended from a massless spring of constant k. When masses are in equilibrium, m_2 is removed without disturbing the system. Find the amplitude of oscillation and angular frequency of m_1

A body is projected in vertically upwards direction with a speed u. Find the time taken

The potential energy of a certain particle is given by U = 30x^2 - 20 y^2 . Find the force acting on the particle.

Electrons move at right angles to a magnetic field of 100 gauss and enter it with a velocity fo 2xx10^10 cms^-1 . Find the radius of their circular path. Given e//m = 1.7 xx 10^7 e.m.u g^-1

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is 0 cm.