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A solide homogeneous cylinder of height ...

A solide homogeneous cylinder of height `h` and base radius `r` is kept vertically on a conveyer belt moving horizontally with an increasing velocity `v=a+bt^(2)`. If the cylinder is not allowed to slip then the time whem the cylinder is about to topple , will be equal to

A

`(rg)/(bh)`

B

`(2rg)/(bh)`

C

`(2bg)/(rh)`

D

`(rg)/(2bh)`

Text Solution

Verified by Experts

The correct Answer is:
A
WRT to belt, pseudo force `ma` acts on cylinder at `COM` as shown about to cylinder will be just about to topple when torque to weight `w.r.t. P.`
`(dv)/(dt)=a=2bt`
`m.2bt. (h)/(2)=mg.r`
`t=(rg)/(bh) Ans. gr//bh`
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