Let $g$ be the acceleration due to gravity at earth's surface and $K$ be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by $2\%$ keeping all other quantities same, then
$g$ decreases by $2\%$ and $K$ decreases by $4\%$
$g$ decreases by $4\%$ and $K$ increases by $2\%$
$g$ increases by $4\%$ and $K$ increases by $4\%$
$g$ decreases by $4\%$ and $K$ increases by $4\%$
Gravitational acceleration on the surface of a planet is $\frac{\sqrt 6}{11}g$ , where $g$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $\frac{2}{3}\, times$ that of the earth. If the escape speed on the surface of the earth is taken to be $11\, kms^{-1}$, the escape speed on the surface of the planet in $kms^{-1}$ will be
At a height of $10 \,km$ above the surface of earth, the value of acceleration due to gravity is the same as that of a particular depth below the surface of earth. Assuming uniform mass density for the earth, the depth is ............. $km$
At a given place where acceleration due to gravity is $‘g’$ $m/{\sec ^2}$, a sphere of lead of density $‘d’$ $kg/{m^3}$ is gently released in a column of liquid of density $'\rho '\;kg/{m^3}$. If $d > \rho $, the sphere will
A planet of radius $R =\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3} \ kgm ^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $=6 \times 10^6 \ m$ and the acceleration due to gravity on Earth is $10 \ ms ^{-2}$ )
The mass of a planet and its diameter are three times those of earth's. Then the acceleration due to gravity on the surface of the planet is ....... $m/s^2$