QUIZ 1:Gravitation (previous Year Q)(#Free Test Series) - JEE MCQ

A mass M is split into two parts, m and (M?m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts [AMU 2000] 

 Suppose the gravitational force varies inversely as the  nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004] 

If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would [IIT 1981; CPMT 1981; MP PMT 1996, 97; Roorkee 1992; MP PET 1999; Kerala PMT 2004] 

The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth [Roorkee 2000] 

 In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g=10ms^-2) and radius of earth is 6400 kms) [Roorkee 2000] 

A simple pendulum has a time period T₁ when on the earth?s surface and T₂ when taken to a height R above the earth?s surface, where R is the radius of the earth. The value of T₂/T₁ is [IIT-JEE 2001] 

A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be [NCERT 1971; CPMT 1971, 97; IIT 1983; CBSE PMT 1991; Kurukshetra CEE 1996; CMEET Bihar 1995; MNR 1998; AIEEE 2004]