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

Assertion: Animate object can accelerate in the absence of external force. 

Reason:  Newton's second law is not applicable on animate object.

• 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 is false.

A block of mass  m  is pulled along a horizontal surface by applying a force at an angle θ with the horizontal. If the block travels with a uniform velocity and has a displacement  d  and the coefficient of friction is  μ  then the work done by the applied force is

• $\frac{\mathrm{\mu } \mathrm{mg} \mathrm{d}}{\mathrm{cos\theta } + \mathrm{\mu } \mathrm{sin\theta }}$

• $\frac{\mathrm{\mu } \mathrm{mg} \mathrm{d} \mathrm{cos\theta }}{\mathrm{cos\theta } + \mathrm{\mu } \mathrm{sin\theta }}$

• $\frac{\mathrm{\mu } \mathrm{mg} \mathrm{d} \mathrm{sin\theta }}{\mathrm{cos\theta } + \mathrm{\mu } \mathrm{sin\theta }}$

• $\frac{\mathrm{\mu } \mathrm{mg} \mathrm{d} \mathrm{cos\theta }}{\mathrm{cos\theta } - \mathrm{\mu } \mathrm{sin\theta }}$

Assertion: A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling motion) 

Reason:  For perfect rolling motion, work done against friction is zero.

• 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

195.

A  ball  is  bouncing  down  a  flight of stairs. The  coefficient  of  restitution  is  e. The  height of  each  step  is  d  and  the  ball  descends one  step  each  bounce. After  each  bounce  it   rebounds  to  a  height h  above  the  next  lower  step. The  height  is  large  enough  compared  with  the  width of  step  so  that  the  impacts  are  effectively  head-on.  Find the  relationship  between  h  and  d.

• h = $\frac{\mathrm{d}}{1 - {\mathrm{e}}^2}$

• h = $\frac{\mathrm{d}}{1 + {\mathrm{e}}^2}$

• h = $\frac{\mathrm{d}}{1 + \mathrm{e}}$

• h = $\sqrt{\frac{\mathrm{d}}{1 - {\mathrm{e}}^2}}$

Assertion:  Angular  speed  of  a  planet  around  the  sun  increases,  when  it  is  closer to the sun.

Reason: Total angular momentum of the system remains 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

A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is

• $\sqrt{\frac{\mathrm{F} \mathrm{r}}{\mathrm{m}}}$

• $\sqrt{\frac{\mathrm{F}}{\mathrm{r}}}$

• $\sqrt{\mathrm{Fmr}}$

• $\sqrt{\frac{\mathrm{F}}{\mathrm{m} \mathrm{r}}}$

A bullet is fired from a rifle and recoils. Kinetic energy of rifile is

• less than K.E of bullet

• greater than K.E of bullet

• equal to K.E of bullet

• none of the above

Figure shows the variation of energy with the orbit radius r of a satellite  in a circular motion. Mark the correct statement

• C is total energy, B kinetic energy and A is potential energy.

• A is kinetic energy, B total energy and C potential energy

• A and 8 are the kinetic and potential energies and C the total energy of the satellite.

• C and A arc kinetic and potential energy respectively and B the total energy of the satellite.

The force of gravitation is

• repulsive

• conservative

• electrostatic

• non-conservative