The planets with radii R₁ and R₂ have densities ρ1, ρ2 respectively. Their atmospheric pressure is p1 and p2 respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of the atmosphere is

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_1}{{\mathrm{\rho }}_2{\mathrm{R}}_1{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{\rho }}_1{\mathrm{R}}_2{\mathrm{\rho }}_2}{{\mathrm{pP}}_2{\mathrm{R}}_1{\mathrm{\rho }}_1}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_1}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_2}$

• $\frac{{\mathrm{p}}_1{\mathrm{R}}_1{\mathrm{\rho }}_2}{{\mathrm{p}}_2{\mathrm{R}}_2{\mathrm{\rho }}_1}$

A thin symmertical double convex lens of refractive index μ₂ = 1.5 is placed between a medium of refractive index μ₁ = 1.4 to the left and another medium of refractive index μ₃ = 1.6 to the right. Then, the system behaves as

• a convex lens

• a concave lens

• a glass plate

• a convexo-concave lens

123.

The escape velocity for the earth is 11.2 km/sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

• 56.0 km/sec

• 280 km/sec

•  112 km/sec

•  56 km/sec

Dimension of relative density is

• kgm^-3

• ML^-3

• dimensionless

• M²L^-6

A ball is thrown from height 'h' and another from '2h'. The ratio of time taken by the two balls to reach ground is

• $1:\sqrt{2}$

• $\sqrt{2}:1$

• 2:1

• 1:2

A ball is thrown upwards, it takes 4sec to reach back to the ground. Find its initial velocity

• 30ms^-1

• 10ms^-1

• 40ms^-1

• 20ms^-1

Acceleration due to gravity at earth's surface is 'g'ms^-2 . Find the effective value of gravity at a height of 32 km from sea level (R_e=6400km)

• 0.5 gms^-2

• 0.99 gms^-2

• 1.01 gms^-2

• 0.90 gms^-2

Near earth's surface, time period of a satelliteis 4 hrs. Find its time period at height '4R' from the centre of earth

• 32 hrs

• $\left(\frac{1}{8\sqrt[3]{2}}\right)\mathrm{hrs}$

• 8$\sqrt[3]{2}$hrs

• 16hrs

The dimensions of gravitational constant are

• $\left[{\mathrm{ML}}^3{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^2\right]$

• $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$

The earth of mass =6×10²⁴ kg revolves around the sun with an angular velocity of 2×10^-7 rad/s in a circular orbit of radius 1.5×10⁸ km. The force exerted by the sun on earth is

• 6×10¹⁹ N

• 18×10²⁵ N

• 36×10²¹ N

• 27×10³⁹ N