The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}$ and ${W_3}$ respectively, then
${W_1} < {W_2} > {W_3}$
${W_1} = {W_2} = {W_3}$
${W_1} < {W_2} < {W_3}$
${W_1} > {W_2} > {W_3}$
Given below are two statements:
Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement $II:$ Acceleration due to earth's gravity is same at a height ' $h$ ' and depth ' $d$ ' from earth's surface, if $h = d$.
In the light of above statements, choose the most appropriate answer form the options given below
A person whose mass is $100\, {kg}$ travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as $10$ ${m} / {s}^{2}$ and $4 \,{m} / {s}^{2}$ respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.
The radii of two planets are respectively ${R_1}$ and ${R_2}$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is
The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g$ = the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth, is
If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ......... $m/{\sec ^2}$ ($ g$ on earth $= 9.8\, m/sec^2$ )