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A force F is given by F=at+bt^(2), where...

A force `F` is given by `F=at+bt^(2)`, where `t` is time. The dimensions of `a and b` are

A

`1/(4pi epsilon_(0))Q^(2)/(mv)`

B

`1/(4piepsilon_(0))(4Q^(2))/(mv^(2))`

C

`1/(4piepsilon_(0))(2Q^(2))/(mv^(2))`

D

`1/(4piepsilon_(0))(3Q^(2))/(mv^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
By mechanical energy conservation
`(PE+KE)_(i)=(PE+KE)_(f)`
`0+1/2 mv^(2)+0=(KQ^(2))/d+1/2 m (v/2)^(2)xx2`
( `:'` from momentum conservation at closet approach, both particle will move with a common speed `v//2`)
`:. D=(4KQ^(2))/(mv^(2))`
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