Question

A horizontal force $F$ pulls a ring of mass $m_1$ such that $\theta$ remains constant with time. The ring is constrained to move along a smooth rigid horizontal wire. A bob of mass $m_2$ hangs from $m_1$ by an inextensible light string. Then match the entries of Column I with that of Column II

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{i.}& F& \text{a.}& (m_1+m_2)g\\ \text{ii.}& \text{Force acting on}{m}_2\text{is}& \text{b.}& m_{2}g\sec \theta \\ \text{iii.}& \text{Tension in the string is}& \text{c.}& m_2\frac{F}{m_1+m_2}\\ \text{iv.}& \text{Force acting on}{m}_1\text{by the wire is}& \text{d.}& (m_1+m_2)g\tan \theta \end{array}$

• A. $i-dii-ciii-biv-a$
• B. $i-dii-biii-civ-a$
• C. $i-cii-diii-biv-a$
• D. $i-dii-biii-civ-a$

Answer 1

The correct option is A $i-dii-ciii-biv-a$


$F=(m_1+m_2)a\left(i\right)$
$T\sin \theta =m_{2}a\left(ii\right)$
$T=m_{2}g\sec \theta \left(iii\right)$
From equation (ii) and (iii) $a=g\tan \theta$
Put in $l$
$F=(m_1+m_2)g\tan \theta$
Net force acting on $m_2=m_{2}a=\frac{m_{2}F}{m_1+m_2}$
Force acting on $m_1$ by wire:
$N=m_{1}g+T\cos \theta =m_{1}g+m_{2}g$