A solid sphere rolls down two different inclined planes of the same height but of different inclinations

Options

A. the speeds will be same but time of descent will be different
B. . in both cases, the speeds and time of descent will be same
C. in both cases, the speeds and time of descent will be same
D. speeds and time of descent both will be different

Answer

A

Explanation

As ` sqrt((2gh)/(1+1/(MR^(2))))`
Hence velocity is independent of te inclination of the plane and depend any on height `h` through which body descends.
But because `t+1/(sintheta)sqrt((2h)/g(1+I/(MR^(2)))` depends on the inclination also, hence greater the inclination lesser will be the time of desced. Hence, in present cae the speeds will be same (became `h` is same) but time is decreased will be difference (because of different inclination)