`(X^(2)/("Mass"))` has the dimensions of kinetic energy. Then X has the dimensions of

Options

A. Pressure
B. Impulse
C. Torque
D. Force

Answer

b

Explanation

`(X^(2))/(m)=K.E.=(1)/(2)mv^(2)`
`therefore X^(2)=(1)/(2)m^(2)v^(2) therefore X=(1)/(sqrt(2))mv`
Thus X has the dimensions of momentum i.e. [`M^(1)L^(1)T^(-1)]`.
Out of the four quantities given above,
Impulse = `(Fxxt)` has the dimensions
`[L^(1)M^(1)T^(-2)xxT^(1)]=[L^(1)M^(1)T^(-1)]`
`therefore` X has the dimensions of impulse.