Question

The velocity of a particle v at an instant t is given by v = at + bt². The dimensions of b is
a) [L]
b) [LT⁻¹]
c) [LT⁻²]
d) [LT⁻³]

Answer 1

Given , velocity of Particle at any instant of time t is given by v = at + bt²
according to rule of dimension ,
dimension of v = dimension of at = dimension of bt²
we know,
dimension of v = [LT⁻¹]
so, dimension of b × dimension of t² = [LT⁻¹]
dimension of b = [LT⁻¹]/[T²] = [LT⁻³]

Hence, option (d) is correct.

Answer 2

The correct option is d.

LT^-3