The length of second pendulum is 1 m on earth. If mass and diameter of the planet is doubled than that of earth, then length becomes:

Options

A. 1 m
B. 4 m
C. 0.5 m
D. 2 m.

Answer

C

Explanation

For seconds pendulum time period in 2 seconds
`therefore 2=2pi sqrt((l)/(m)) & 2=2pi sqrt((l.)/(m.))`
`therefore (l)/(g)=(l.)/(g.) rArr l.=l.(g.)/(g)=l.(M.)/(M)xx(R^(2))/(R.^(2))=2.(1)/(4).l`
`rArr l.=0.5l=0.5 xx 1m=0.5m`
Correct choice is (c ).