11.

A body of mass 5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k = 5 N/m. The maximum compression of the spring would be

• 0.5 m

• 0.15 m

• 1.5 m

• 0.12 m

Neglecting  the  density  of  air, the  thermal  velocity  obtained  by  a  raindrop  of  radius  0.3  nm  falling  through  air  of  viscosity  1.8 × 10⁵ N s m²  will  be

• 10.9 m s^-1

• 7.48  m s^-1

• 3.7 m s^-1

• 12.8 m s^-1

A  particle  executes  simple  harmonic  motion  of  period T  and amplitude  l along  a  rod  AB  of  length  2l. The  rod  AB  itself executes  simple  harmonic  motion of the same period and  amplitude  in  a  direction  perpendicular  to  its  length.  Initially, both the  particle  and the  rod  are  in  their  mean  positions. The  path  traced  out  by  the  particle  will  be 

• a circle of radius l

• a straight line inclined at $\frac{\mathrm{\pi }}{4}$ to the rod

• an ellipse

• a figure of eight

When a current is passed in a conductor, 3^o C rise in temperature is observed. If the strength of current is made thrice, then rise in temperature will approximately be

• 36^oC

• 27^o C

• 18^o C

• 9^o C

In  a  metal  with  positive  Thomson  coefficient, current is  passed  from  the  lower  temperature  to  higher   temperature  to  higher  temperature  side. The  heat  will   be

• absorbed

• constant

• evolved

• either 'b' or 'c'

A ball is suspended  by  a  thread  of  length  L  at  the  point  O  on  a  wall  which  is  inclined  to  the  vertical  $\mathrm{\alpha }$. The  thread with  the ball is  displaced  by  a  small  angle  β  away  from  the  wall. If  the  ball  is  released, the  period  of  oscillation  of  the  pendulum  when   β > $\mathrm{\alpha }$ will be

• $\sqrt{\frac{\mathrm{L}}{\mathrm{g}}} \left[\mathrm{\pi } + 2 {\sin }^{-1} \frac{\mathrm{\alpha }}{\mathrm{\beta }}\right]$

• $\sqrt{\frac{\mathrm{L}}{\mathrm{g}}} \left[\mathrm{\pi } - 2 {\sin }^{-1} \frac{\mathrm{\beta }}{\mathrm{\alpha }}\right]$

• $\sqrt{\frac{\mathrm{L}}{\mathrm{g}}} \left[2 {\sin }^{-1} \frac{\mathrm{\beta }}{\mathrm{\alpha }} - \mathrm{\pi }\right]$

• $\sqrt{\frac{\mathrm{L}}{\mathrm{g}}} \left[ {\sin }^{-1} \frac{\mathrm{\alpha }}{\mathrm{\beta }} + \mathrm{\pi } \right]$

Assertion:  Liquid molecules have greater potential energy at the melting point.

Reason:  Intermolecular spacing between molecules increases at melting point.

• 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.

Assertion:  The bob of a simple pendulum is a ball full of water, if a fine hole is made in the bottom of the ball, the time period first increases and then decreases.  

Reason: As water flows out of the bob the weight of bob decreases.

• 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.

Assertion:  For  an  isothermal  process  in  an  ideal  gas,  the heat  obsorbed  by the  gas is  entirely  used   in  the  work  done  by  the  gas. 

Reason:  During  a  process  taking  place in  a  system, the temperature remains constant then the  process is isothermal.

• 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

Assertion:   When hot  water  is  poured  in  a  beaker of  thick  glass,  the  beaker cracks. 

Reason:  Outer surface of the beaker expands suddenly.

• 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