How much momentum will a dumbbell of mass $10 \, kg$ transfer to the floor,if it falls from a height of $0.8 \, m$? Take acceleration due to gravity as $10 \, m s^{-2}$.

$A$ planet existed whose mass and radius were both half of the Earth. What would be the acceleration due to gravity at the surface of the planet in terms of that on the surface of the Earth?

Gravitational force on an imaginary planet is six times stronger than the gravitational force of the Earth. Determine the value of acceleration due to gravity and the weight of an object of mass $50 \, kg$ on that planet.

The acceleration due to gravity at the moon's surface is $1.67 \, m s^{-2}$. If the radius of the moon is $1.74 \times 10^{6} \, m$,calculate the mass of the moon. (Use $G = 6.67 \times 10^{-11} \, N m^{2} kg^{-2}$)

An object is dropped from rest at a height of $150 \, m$ and simultaneously another object is dropped from rest at a height of $100 \, m$. What is the difference in their heights after $2 \, s$ if both objects drop with the same acceleration? How does the difference in heights vary with time?

If the earth stops rotating,the value of '$g$' at the equator will: