The spool shown in figure is placed on rough horizontal surface and has inner radius $r$ and outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $(\theta )$ for which the spool does not roll and remains stationary is given by
The spool shown in figure is placed on rough horizontal surface and has inner radius $r$ and outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $(\theta )$ for which the spool does not roll and remains stationary is given by
- A
$\theta = cos^{-1} \left( {\frac{r}{R}} \right)$
- B
$\theta = cos^{-1}$$\left( {\frac{{2r}}{R}} \right)$
- C
$\theta = cos^{-1}$$\sqrt {\frac{r}{R}} $
- D
$\theta = sin^{-1}$$\left( {\frac{r}{R}} \right)$
Similar Questions
$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $‘m’$ and side $‘a’$ which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between lines of action of $‘mg’$ and normal reaction $‘N’$ is :
$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $‘m’$ and side $‘a’$ which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between lines of action of $‘mg’$ and normal reaction $‘N’$ is :
A uniform rod of length $200 \,\mathrm{~cm}$ and mass $500 \,\mathrm{~g}$ is balanced on a wedge placed at $40\,cm$ mark. A mass of $2\, \mathrm{~kg}$ is suspended from the rod at $20\, \mathrm{~cm}$ and another unknown mass $'m'$ is suspended from the rod at $160\, \mathrm{~cm}$ mark as shown in the figure. Find the value of $'m'$ such that the rod is in equilibrium. $\left(\mathrm{g}=10 \,\mathrm{~m} / \mathrm{s}^{2}\right)$
A uniform rod of length $200 \,\mathrm{~cm}$ and mass $500 \,\mathrm{~g}$ is balanced on a wedge placed at $40\,cm$ mark. A mass of $2\, \mathrm{~kg}$ is suspended from the rod at $20\, \mathrm{~cm}$ and another unknown mass $'m'$ is suspended from the rod at $160\, \mathrm{~cm}$ mark as shown in the figure. Find the value of $'m'$ such that the rod is in equilibrium. $\left(\mathrm{g}=10 \,\mathrm{~m} / \mathrm{s}^{2}\right)$
- [NEET 2021]
A uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$ . The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge ?
A uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$ . The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge ?
$A$ rod of weight $w$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at a distance $x$ from $A$.
$A$ rod of weight $w$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at a distance $x$ from $A$.
Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body, which is then pivoted as shown in figure. If in equilibrium the body is in the shown configuration, ratio $M/m$ will be
Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body, which is then pivoted as shown in figure. If in equilibrium the body is in the shown configuration, ratio $M/m$ will be