Question

Which of the following are correct expression for torque acting on a body? 
A. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{L}}$ 
B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$ 
C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$ 
D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$ 
E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$ 
( $\ddot{r}=$ position vector; $\dot{\mathrm{p}}=$ linear momentum; $\ddot{\mathrm{L}}=$ angular momentum; $\ddot{\alpha}=$ angular acceleration; $\mathrm{I}=$ moment of inertia; $\ddot{\mathrm{F}}=$ force; $\mathrm{t}=$ time $)$ 
Choose the correct answer from the options given below:

• A. B, D and E Only
• B. C and D Only
• C. B, C, D and E Only
• D. A, B, D and E Only

Hint:

Torque can be expressed in terms of position vector, linear momentum, angular momentum, and force.

Answer 1

The Correct Option is C

1. Correct expressions for torque: 
- B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$ 
- C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$ 
- D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$ 
- E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$ 
Therefore, the correct answer is (3) B, C, D and E Only.