Experimental investigations show that the intensity of solar radiation is maximum for a wavelength 480 nm in the visible region. Estimate the surface temperature of sun. (Given Wien's constant b = 2.88 x 10^-3 mK.)

• 4000 K

• 6000 K

• 8000 K

• 10⁶ K

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the root mean square speed of gas molecules is v, then at 480 K, it will be

• 4v

• 2v

• $\frac{\mathrm{v}}{2}$

• $\frac{\mathrm{v}}{4}$

13.

n identical droplets are charged to V volt  each. if they coalesce to form a single drop, then its potential will be

• n^2/3V

• n^1/3V

• nV

• V/n

A particle of mass m is attached to three identical massless springs of spring constant k as shown in the figure. The time period of vertical oscillation of the particle is

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{2\mathrm{k}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{3\mathrm{k}}}$

• $\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

A spring of force constant k is cut into three equal parts. The force constant of each part would be

• $\frac{\mathrm{k}}{3}$

• 3k

• k

• 2k

A body floats in water with 40% of its volume outside water. When the same body floats in oil, 60% of its volume remains outside oil. The relative density of the oil is

• 0.9

• 1.2

• 1.5

• 1.8

A uniform long tube is bent into a circle of radius R and it lies in vertical plane. Two liquids of same volume but densities ρ and δ fill half the tube. The angle θ is

• ${\tan }^{-1} \left(\frac{\mathrm{\rho } - \mathrm{\delta }}{\mathrm{\rho } + \mathrm{\delta }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\rho }}{\mathrm{\delta }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\delta }}{\mathrm{\rho }}\right)$

• ${\tan }^{-1} \left(\frac{\mathrm{\rho } + \mathrm{\delta }}{\mathrm{\rho } - \mathrm{\delta }}\right)$

Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocities are v and nv, then value of n is

• 16

• 8

• 4

• 2

A particle is executing linear simple harmonic motion of amplitude A. At what displacement is the energy of the particle half potential and half kinetic ?

• $\frac{\mathrm{A}}{4}$

• $\frac{\mathrm{A}}{2}$

• $\frac{\mathrm{A}}{\sqrt{2}}$

• $\frac{\mathrm{A}}{\sqrt{3}}$

The equation of a progressive wave is$\mathrm{y} = 4 \sin (4\mathrm{\pi t} - 0.04\mathrm{x} + \mathrm{\pi }/3)$ where x is in metre and t is in second. The velocity of the wave is

• $100 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $50 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $25 \mathrm{\pi } \mathrm{m}/\mathrm{s}$

• $\mathrm{\pi } \mathrm{m}/\mathrm{s}$