A smooth rod of length $l$ is kept inside a trolley at an angle $\theta$ as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
$g\, tan\theta$
$g\, cos\theta$
$g\, sin\theta$
$g\, cot\theta$
A uniform rod $AB$ is suspended from a point $X$, at a variable distance from $x$ from $A$, as shown. To make the rod horizontal, a mass $m$ is suspended from its end $A$. A set of $(m, x)$ values is recorded. The appropriate variable that give a straight line, when plotted, are
A uniform meter scale is supported from its $20\ cm$ mark. A body suspended from $10\ cm$ mark keeps the scale horizontal. However, the scale gets unbalanced if the body is completely immersed in water. To regain the balance the body is shifted to the $8\ cm$ mark. Therefore, the specific gravity of the material of the body is
Can a body will remain in partial equilibrium ? Explain with illustration.
$A$ body weighs $6$ gms when placed in one pan and $24$ gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is ....... $gm$.
A massless string is wrapped round a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be