A tunnel is dug through the centre of the earth. Show that a body of mass m when dropped from rest from one end of the tunnel will execute simple harmonic motion.

One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump isremoved, the column of mercury in the U-tube executes simple harmonic motion.

Total charge -Q is uniformaly spread along length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring. Show that the particly executes a simple harmonic oscillation.

A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20 A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure. Shown that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

An object of mass m is raised from the surface of the earth to a heigt equal to the radius of the earth , that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

A body is dropped from rest at a height of 150 m and simultaneously another body is dropped from rest from a point 100 m above the ground. What is their difference in height after they have fallen 2s? How does the differences in height vary with time.

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. the acceleration of the mass at the instant when the velocity of the rod is half the terminal velocity.

A pair of parallel horizontal conducting rails of negligible resistance shorted at one end is fixed on a table. The distance between the rails is L. A conducting massless rod of resistance R can slide on the rails frictionlessly. The rod is tied to a massless string which passes over a pulley fixed to the edge of the table, A mass m, tied to the other end of the string hanges vertically. A constant magnetic field B exists perpendicular to the table. If the system is released from rest, calculate. the terminal velocity achieved by the rod.

A stone of mass and spring constant k. The unstrecthed length of the string is L and has negligible mass. The other end of the string is fixed to a nail at a point P. Initially the stone is at the same level as the point P. The stone is dropped vertically from point P. Find the distance y from the top when the mass comes to rest for an instant, for the first time.

A particle A has chrage +q and a particle B has charge +4q with each of them having the same mass m. When allowed to fall from rest through the same electric potential difference, the ratio of their speed (v_(A))/(v_(B)) will become