Which of the following are correct expressions for torque acting on a body? A. B. C. D. E. ( = position vector; = linear momentum; = angular momentum; = angular acceleration; = moment of

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Solution

Q.
Which of the following are correct expressions for torque acting on a body

A. $\vec{τ} = \vec{r} \times \vec{L}$ B. $\vec{τ} = \frac{d}{d t} (\vec{r} \times \vec{p})$

C. $\vec{τ} = \vec{r} \times \frac{d \vec{p}}{d t}$ D. $\vec{τ} = I \vec{α}$

E. $\vec{τ} = \vec{r} \times \vec{F}$

( $\vec{r}$ = position vector; $\vec{p}$ = linear momentum; $\vec{L}$ = angular momentum;

$\vec{α}$ = angular acceleration; $I$ = moment of inertia; $\vec{F}$ = force; t = time)

Choose the correct answer from the options given below: [2025]

1 B, D and E Only

2 C and D Only

3 B, C, D and E Only

4 A, B, D and E Only

Ans.
(3)

$\vec{τ} = \vec{r} \times \vec{L}$ wrong

$\vec{τ} = \frac{d}{d t} (\vec{r} \times \vec{p})$ correct

$\vec{τ} = \vec{r} \times \frac{d \vec{p}}{d t} = \vec{r} \times \vec{F}$ correct

$\vec{τ} = I \vec{α}$ correct

$\vec{τ} = \vec{r} \times \vec{F}$ correct

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