11.

The observed wavelength of light coming from a distant galaxy is found to be increased by 0.5% as compared with that coming from a
terrestrial source. The galaxy is

• stationary with respect to the earth

• approaching the earth with velocity of light

• receding from the earth with velocity of light

• receding from the earth with a velocity
  equal to 1.5 10⁶ m/s.

A body weighs 200 N at the surface of earth. If it be placed in an artificial satellite revolving at height where acceleration due to gravity is half of that at earth's surface. It will weigh

• 2$\times$10⁹ N/m²

• 2 $\times$10⁸ N/m²

• 2$\times$10⁶ N/m²

• 2$\times$ 10⁴ N/m²

A simple pendulum is made by attaching a 1 kg bob to a 5 m long copper wire. Its period is T. Now, if 1 kg bob is replaced by 10 kg bob, the period of oscillations

• remains T

• becomes greater than T

• becomes less than T

• any of the above depends on gravity

A metal wire of length l, area of cross-section A and Young's modulus Y behaves as a spring of spring constant k given by

• $\mathrm{k}= \frac{\mathrm{YA}}{\mathrm{l}}$

• $\mathrm{k}= \frac{2\mathrm{YA}}{\mathrm{l}}$

• $\mathrm{k}= \frac{\mathrm{YA}}{2\mathrm{l}}$

• $\mathrm{k}= \frac{\mathrm{Yl}}{\mathrm{A}}$

The length of a second's pendulum is

• 99.8 cm

• 99 cm

• 100 cm

• None of the above

The length of a needle floating on water is 2.5 cm. Calculate the added force (due to surface tension) required to pull the needle out of water. (Surface tension of water = 7.2$\times$ 10^-2 N/m²)

• 3.6 $\times$ 10^-3 N

• 3.4 $\times$ 10^-10 N

• 3.0 $\times$ 10^-5 N

• 3.8 $\times$ 10^-11 N

A capillary tube of radius r is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is m. If the capillary of radius 2r is taken and dipped in water, the mass of water that will rise in the capillary tube will be

• m

• 2 m

• m/2

• 4 m

A metallic solid sphere is rotating about its diameter as axes of rotation. If the temperature is increased by 200°C, the percentage increase in its moment of inertia is (Coefficient of linear expansion of the metal = ${10}^{-5}/°\mathrm{C}$)

• 0.1%

• 0.2%

• 0.3%

• 0.4%

The average velocity of the molecules in a gas in equilibrium is

• proportional to $\sqrt{\mathrm{T}}$

• proportional to T

• proportional to T²

• equal to zero

A vessel containing 0.1 m³ of air at 76 cm of Hg is connected to an evacuated vessel of capacity 0.09m³. The resultant air pressure is

• 20 cm of Hg

• 30 cm of Hg

• 40 cm of Hg

• 60 cm of Hg