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The velocity v of a particle at time t i...

The velocity `v` of a particle at time `t` is given by `v=at+(b)/(t+c)`, where `a, b and c` are constants. The dimensions of `a, b and c` are, respectively.

A

`LT^(-2), L and T`

B

`L^(2), T and LT^(2)`

C

`LT^(2), LT and L`

D

`L, LT and T^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`v=at + (b)/(t+c)`
Dimensionally
at = `v rArr a[T] = [LT^(-1)]rArr a = [LT^(-2)]`
`c = t rArr c = [M^(0)L^(0) T^(1)]`
`(b)/(t+c) = v rArr (b)/(T) = [LT^(-1)] rArr b= [M^(0)L^(1)T^(0)]`
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Knowledge Check

  • The position of particle at time t is given by, x(t) = (v_(0)//prop) (1-e^(-ut)) where v_(0) is a constant prop gt 0 . The dimension of v_(0) and prop are,

    A
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    B
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    C
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    D
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