11.

A sphere rolls down an inclined plane of inclination θ. What is the acceleration as the sphere reaches the bottom?

• $\frac{5}{7}\mathrm{g} \mathrm{sin\theta }$

• $\frac{3}{5}\mathrm{g} \mathrm{sin\theta }$

• $\frac{2}{7}\mathrm{g} \mathrm{sin\theta }$

• $\frac{2}{5}\mathrm{g} \mathrm{sin\theta }$

In a bicycle, the radius of rear wheel is twice the radius of front wheel. If r_f and r_r are the radii, v_f and v_r are the speeds of topmost points of the wheel, then:

• v_r = 2v_f

• v_f = 2v_r

• v_r = v_f

• v_f > v_r

Moment of inertia of an object does not depend upon :

• mass of the object

• mass distribution

• angular velocity

• axis of rotation

A particle falls towards earth from infinity. Its velocity on reaching the earth would be:

• infinity

• $\sqrt{2\mathrm{gR}}$

• $2\sqrt{\mathrm{gR}}$

• zero

Two bodies of mass m and 4m have equal kinetic energy. What is the ratio of their momentum?

• 1 : 4

• 1 : 2

• 1 : 1

• 2 : 1

According to Kepler's law, the time period of a satellite varies with its radius are as:

• T² ∝ R³

• T³ ∝ R²

• ${\mathrm{T}}^2 \propto \frac{1}{{\mathrm{R}}^3}$

• ${\mathrm{T}}^3 \propto \frac{1}{{\mathrm{R}}^2}$

A particle is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point :

• the momentum changes by mv

• the momentum changes by 2mv

• the kinetic energy changes by 1/2 mv²

• the kinetic energy changes by mv²

The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble, the required surface energy in doing so is given by:

• 32πR²T

• 24πR²T

• 8πR²T

• 4πR²T

Mercury boils at 367°C. However, mercury thermometers are made such that they can measure temperature upto 500°C. This is done by:

• maintaining vacuum above the mercury column in the stem of the thermometer

• filling nitrogen gas at high pressure above the mercury column

• filling oxygen gas at high pressure above the mercury column

• filling nitrogen gas at low pressure above the mercury column

An ice-cube of density 900 kg/m³ is floating in the water of density 1000 kg/m³ The percentage of volume of the ice-cube outside the water is:

• 20 %

• 35 %

• 10 %

• 25 %