The motion of planets in the solar system is an example of the conservation of

• mass

• linear momentum

• angular momentum

• energy

Assertion: The earth is slowing down and as a result the moon is coming nearer to it.

Reason: The angular momentum of the earth moon system is not conserved.

• if both assertion and reason are true and the reason is the correct explanation of the assertion

• if both assertion and reason are true and the reason is not the correct explanation of the assertion

• if assertion is true but reason is false

• if both assertion and reason are false statements

Assertion: The length of the day is slowly increasing. 

Reason: The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

• if both assertion and reason are true and the reason is the correct explanation of assertion

• if both assertion and reason are true and the reason is not the correct explanation of the assertion

• if assertion is true but reason is false

• if both assertion and reason are false statements

114.

The dimension of torque is

• [ M L^-2 ]

• [ M L^-1 T^-1 ]

• [ M L² T^-2 ]

• [ M L³ T^-3 ]

The angular momentum of a moving body remains constant if

• net external force is applied

• net external torque is applied

• net pressure is applied

• net external torque is not applied

A conducting sphere of radius 1O cm is charged with 10 μC. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

• 1 : 4

• 1 : 2

• 1 : 3

• 1 : 1

Two masses are attached to a rod end to end. If torque is applied they rotate with angular acceleration $\mathrm{\alpha }$. If their distances are doubled  and same torque is applied, then they move with angular acceleration

• 4 α

• α

• 3 α

• α/4

A body of mass M moving with velocity V explodes into two equal parts. Id one comes to rest and the other moves with velocity v, what would be the value of v?

• V

• $\frac{\mathrm{V}}{\sqrt{2}}$

• 4V

• 2V

If the earth is treated as a sphere of  radius R and mass M, its angular momentum about the axis of rotation with period T, is

• $\frac{\mathrm{M} {\mathrm{R}}^2 \mathrm{T}}{2\mathrm{\pi }}$

• $\frac{4\mathrm{\pi } \mathrm{M} {\mathrm{R}}^2}{5\mathrm{T}}$

• $\frac{\mathrm{\pi } \mathrm{M} {\mathrm{R}}^3}{\mathrm{T}}$

• $\frac{2\mathrm{\pi } \mathrm{M} {\mathrm{R}}^2}{\mathrm{T}}$

A spherical solid ball of mass 1 kg and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s. The kinetic energy of rotation is

• 4500J

• 90J

• 910J

• 0.45J