Gravitation

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

The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance 5×10¹¹m will be (charge on electron =1.6×10^-19 C, mass of electron =9.1×10^-31 kg, mass of proton =1.6×10^-27 kg, G=6.7×10^-11 Nm²/kg² )

• 2.36×10³⁹

• 2.36×10⁴⁰

• 2.36×10⁴¹

• 2.34×10⁴²

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

• $\frac{1}{\mathrm{R}}$

• $\frac{1}{\sqrt{\mathrm{R}}}$

• R

• $\frac{1}{{\mathrm{R}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

Two planets are revolving around the earth with velocities v₁ and v₂ and in radii r₁ and r₂ ( r₁ > r₂ ) respectively. Then :

• v₁ = v₂

• v₁ > v₂

• v₁ < v₂

• $\frac{{\mathrm{v}}_1}{{\mathrm{r}}_1} =\frac{{\mathrm{v}}_2}{{\mathrm{r}}_2}$