A rod of linear mass density 'λ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is.
Which of the following are correct expression for torque acting on a body?
A. $\vec{\tau}=\vec{r} \times \vec{L}$
B. $\vec{\tau}=\frac{d}{d t}(\vec{r} \times \vec{p})$
C. $\vec{\tau}=\vec{r} \times \frac{d \vec{p}}{d t}$
D. $\vec{\tau}=I \vec{\alpha}$
E. $\vec{\tau}=\vec{r} \times \vec{F}$
( $\vec{r}=$ position vector; $\vec{p}=$ linear momentum; $\vec{L}=$ angular momentum; $\vec{\alpha}=$ angular acceleration; $I=$ moment of inertia; $\vec{F}=$ force; $t=$ time)
Choose the correct answer from the options given below:
If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $\vec{r}=a(\hat{i} \cos \omega t+\hat{j} \sin \omega t)$. The direction of force is
A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is