$A$ small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta$ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$, then:
- Athe tension in the string as the sphere passes the $90^o$ position $B$ is equal to $m\left( \frac{u^2}{l} + g \sin \theta \right)$
- Bthe tension in the string at the bottom most position $C$ is equal to $m\left( \frac{u^2}{l} + 5g \sin \theta \right)$
- Cthe tension in the string as the sphere passes the $90^o$ position $B$ is equal to $m\left( \frac{u^2}{l} - 3g \sin \theta \right)$
- Dthe tension in the string at the bottom most position $C$ is equal to $m\left( \frac{u^2}{l} - 5g \sin \theta \right)$
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View Solution$A$ particle of mass $m$ is released from a height $H$ on a smooth curved surface which ends into a vertical loop of radius $R$,as shown. If $\theta$ is the instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical,then identify the correct statement$(s)$ related to the normal reaction $N$ between the block and the surface.
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View Solution$A$ body of mass $0.4\, kg$ is whirled in a vertical circle making $2\, rev/sec$. If the radius of the circle is $2\, m$,then tension in the string when the body is at the top of the circle,is ......... $N$.
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View Solution$A$ stone of mass $150 \ g$ moves in a vertical circle at the end of a string. The radius of the circle is $70 \ cm$ and the speed of the stone at the topmost point $P$ is $3.5 \ m/s$. For the instant at which the stone passes through the highest point $P$,the centripetal force is nearly ......... $N$ (take $g = 10 \ m/s^2$).
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View Solution$A$ stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$. The net forces at the lowest and highest points of the circle directed vertically downwards are:
Lowest Point Highest Point $(a) \ mg - T_1$ $mg + T_2$ $(b) \ mg + T_1$ $mg - T_2$ $(c) \ mg + T_1 - \frac{mv_1^2}{R}$ $mg - T_2 + \frac{mv_2^2}{R}$ $(d) \ mg - T_1 - \frac{mv_1^2}{R}$ $mg + T_2 + \frac{mv_2^2}{R}$
$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.
| Lowest Point | Highest Point |
| $(a) \ mg - T_1$ | $mg + T_2$ |
| $(b) \ mg + T_1$ | $mg - T_2$ |
| $(c) \ mg + T_1 - \frac{mv_1^2}{R}$ | $mg - T_2 + \frac{mv_2^2}{R}$ |
| $(d) \ mg - T_1 - \frac{mv_1^2}{R}$ | $mg + T_2 + \frac{mv_2^2}{R}$ |
$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.
Medium
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