In the case of rotational dynamics,which one of the following statements is correct?
$[\vec{\omega} = \text{angular velocity}, \vec{v} = \text{linear velocity}, \vec{r} = \text{radius vector}, \vec{\alpha} = \text{angular acceleration}, \vec{a} = \text{linear acceleration}, \vec{L} = \text{angular momentum}, \vec{p} = \text{linear momentum}, \vec{\tau} = \text{torque}, \vec{f} = \text{force}]$

  • A
    $\vec{v} = \vec{r} \times \vec{\omega}, \vec{\alpha} = \vec{r} \times \vec{a}, \vec{L} = \vec{r} \times \vec{p}, \vec{\tau} = \vec{f} \times \vec{r}$
  • B
    $\vec{v} = \vec{\omega} \times \vec{r}, \vec{\alpha} = \vec{a} \times \vec{r}, \vec{L} = \vec{p} \times \vec{r}, \vec{\tau} = \vec{r} \times \vec{f}$
  • C
    $\vec{v} = \vec{\omega} \times \vec{r}, \vec{\alpha} = \vec{a} \times \vec{r}, \vec{L} = \vec{r} \times \vec{p}, \vec{\tau} = \vec{r} \times \vec{f}$
  • D
    $\vec{v} = \vec{\omega} \times \vec{r}, \vec{\alpha} = \vec{a} \times \vec{r}, \vec{L} = \vec{p} \cdot \vec{r}, \vec{\tau} = \vec{r} \times \vec{f}$

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Similar Questions

$A$ uniform rod of mass $m$ and length $\ell$ hinged at end $A$ is released from the horizontal position shown in the figure. Just after the rod is released:
Column $I$Column $II$
$(A)$ Angular acceleration of $C$$(P)$ $\frac{3g}{2}$
$(B)$ Angular acceleration of $B$$(Q)$ $\frac{3g}{2\ell}$
$(C)$ Acceleration of $C$$(R)$ $\frac{3g}{4}$
$(D)$ Acceleration of $B$$(S)$ $\frac{3g}{\ell}$

The position of an object having mass $0.1 \text{ kg}$ as a function of time $t$ is given as $\vec{r} = (10t^2\hat{i} + 5t^3\hat{j}) \text{ m}$. At $t = 1 \text{ s}$,which of the following statements are correct?
$A$. The linear momentum $\vec{p} = (2\hat{i} + 1.5\hat{j}) \text{ kg} \cdot \text{m/s}$.
$B$. The force acting on the object $\vec{F} = (2\hat{i} + 3\hat{j}) \text{ N}$.
$C$. The angular momentum of the object about its origin $\vec{L} = 15\hat{k} \text{ J} \cdot \text{s}$.
$D$. The torque acting on the object about its origin $\vec{\tau} = 20\hat{k} \text{ N} \cdot \text{m}$.
Choose the correct answer from the options given below:

$A$ uniform rod of mass $M$ is hinged at its upper end. $A$ particle of mass $m$ moving horizontally strikes the rod at its mid-point elastically. If the particle comes to rest after the collision,find the value of $M/m$.

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$A$ mass $M = 40 \ kg$ is fixed at the very edge of a long plank of mass $80 \ kg$ and length $1 \ m$ which is pivoted such that it is in equilibrium. How far (approx.) from the pivot should a mass of $100 \ kg$ be attached so that the plank starts rotating with an angular acceleration of $1 \ rad/s^2$?

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$A$ cubical block of side $a = 30\,cm$ is moving with velocity $v = 2\,m/s$ on a smooth horizontal surface. The surface has a small bump at a point $O$ as shown in the figure. The angular velocity (in $rad/s$) of the block immediately after it hits the bump is:

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