Questions in gravitation

Select	Question
	If the earth rotates faster than its present speed, the weight of an object will
	If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be
	The moon's radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is
	R is the radius of the earth and $\omega$ is its angular velocity and ${g_p}$ is the value of g at the poles. The effective value of g at the latitude $\lambda = 60^\circ$ will be equal to
	The depth d at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the surface, is [R = radius of the earth]
	At what height over the earth's pole, the free fall acceleration decreases by one percent (assume the radius of earth to be 6400 km)
	The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio
	At what altitude in metre will the acceleration due to gravity be 25% of that at the earth's surface (Radius of earth = R metre)
	If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole
	At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct