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A sphere and circular disc of same mass ...

A sphere and circular disc of same mass and radius are allowed to roll down an inclined plane from the same height without slipping. Find the ratio of times taken by these two to come to the bottom of incline :

A

`15: 14`

B

`sqrt15: sqrt14`

C

`14: 15`

D

`sqrt14: sqrt15`

Text Solution

Verified by Experts

The correct Answer is:
D
Time of descent `t= (1)/(sin theta) sqrt((2h)/(g) (1 + (k^(2))/(R^(2)))) therefore (t_("sphere"))/(t_("disc")) = sqrt(((1+ (k^(2))/(R^(2)))_("sphere"))/((1+ (k^(2))/(R^(2)))_("disc")))= sqrt((1+(2)/(5))/(1+ (1)/(2)))= sqrt((7)/(5) xx (2)/(3))= sqrt((14)/(15))`
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