A ball of mass m is tied up with string and rotated along a horizontal circle of radius r. At an instant, its velocity is ν, and tension in string is T, the force required for circular motion is

• T - m v²/2

• T + m v²/2

• m v²/r

• zero

A dipole of dipole moment 'p' is placed in non-uniform electric field along x-axis. Electric field is increasing at the rate of 1 V m^-1 then the force on dipole is

• 0

• 2p

• p/2

• p

Dimensional formula of angular momentum is

• [ M L² T^-1 ]

• [ M² L² T^-2 ]

• [ M L² T^-3 ]

• [ M L T^-1 ]

Relation between magnetic moment and angular velocity is

• M ∝ ω

• M ∝ ω²

• M ∝ $\sqrt{\mathrm{\omega }}$

• None of these

5.

Gravitational potential of the body of mass m at a height h from surface of earth of radius R is (Take g = acceleration due to gravity at earth's surface)

• - g(R + h )

• - g ( R + h )

• g  ( R + H )

• g ( R - h )

Given that force  $\left( 5\hat{\mathrm{i}} + 7\hat{\mathrm{j}} - 3\hat{\mathrm{k}} \right)$N  acts on a particle at position  $\left( \hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}} \right)$m. Find torque of this force on the particle about origin.

• $4\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$

• $2\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$

• $5\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

• $6\hat{\mathrm{i}} - 4\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$

A particle is projected from the ground with an initial speed of 'v' at angle θ  with horizontal. The average velocity of the particle between its point of projection and height point of trajectory is

• 

• 

• 

• vcosθ

If a vector $2 \hat{\mathrm{i}} + 3 \hat{\mathrm{j}} + 8 \hat{\mathrm{k}}$ is perpendicular to the vector $4 \hat{\mathrm{i}} - 4 \hat{\mathrm{j}} + \mathrm{\alpha } \hat{\mathrm{k}}$, then value of α is

• -1

• $\frac{1}{2}$

• $- \frac{1}{2}$

• 1

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

• 3mgR

• $\frac{1}{3} \mathrm{mgR}$

• 2 mgR

• $\frac{2}{3} \mathrm{mgR}$

Assertion: Moment of inertia is always constant. 

Reason:  Angular moment is conserved that is why moment of inertia is constant.

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

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.