The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a pendulum on this plenet. If it is a 2 second's pendulum on earth?

Options

A. `1// sqrt(2)s`
B. `2 sqrt(2)s`
C. `2s`
D. `1//2 s`

Answer

B

Explanation

Gravity, `g=(GM)/(R^(2))` (G is constant)
`therefore" "(g_("earth"))/(g_("planet"))=(M_(e))/(M_(p))xx(R_(p)^(2))/(R_(e)^(2))`
`(g_(e))/(g_(p))=(2)/(1)`
Also, `T prop (1)/(sqrt(g))rArr(T_(e))/(T_(p))=sqrt((g_(p))/(g_(e)))`
`rArr" "(2)/(T_(p))=sqrt((1)/(2))rArr T_(p)= 2 sqrt(2)s`