$\therefore $ Force required just to move up ${F_{up}} = mg(\sin \theta + \mu \cos \theta )$
Similarly for down ward motion a $ = g(\sin \theta - \mu \cos \theta )$
$\therefore $ Force required just to prevent the body sliding down ${F_{dn}} = mg(\sin \theta - \mu \cos \theta )$
According to problem ${F_{up}} = 2{F_{dn}}$
$⇒$ $mg(\sin \theta + \mu \cos \theta ) = 2mg(\sin \theta - \mu \cos \theta )$
$⇒$ $\sin \theta + \mu \;\cos \theta = 2\sin \theta - 2\mu \;\cos \theta $
$⇒$ $3\mu \cos \theta = \sin \theta $
$⇒$ $\tan \theta = 3\mu $
$⇒$ $\theta = {\tan ^{ - 1}}(3\mu ) = {\tan ^{ - 1}}(3 \times 0.25) = {\tan ^{ - 1}}(0.75)$$ = 36.8^\circ $
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
If a student plots graphs of the square of maximum charge $( Q_{Max} ^2 )$ on the capacitor with time$(t)$ for two different values $L_1$ and $L_2 (L_1 > L_2)$ of $L$ then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)