Question

Suppose, the torque acting on a body is given by $\tau =KL+MI/w$. Where $L$ $=$ angular momentum, $I$ $=$ moment of inertia, $w$ $=$ angular speed. The dimensional formula for $KM$ is same as that for:

• A. ${time}^2$
• B. ${time}^4$
• C. ${time}^{-2}$
• D. ${time}^{-4}$

Answer 1

Answer: (D)

${time}^{-4}$

$\tau =KL+\frac{MI}{W}$
$\tau =M^1{L}^2{T}^{-2}=KL=K{M}^1{L}^2{T}^{-1}$
$\Rightarrow K=T^{-1}$
$\Rightarrow \frac{MI}{W}=M^1{L}^2{T}^{-2}$
$\Rightarrow \frac{M\left(M^1{L}^2\right)}{T^{-1}}=M^1{L}^2{T}^{-2}$
$\Rightarrow M=T^{-3}$
$So,KM=T^{-4}$