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A horizontal force F pulls a ring of mass $m_{1}$ such that $θ$ 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

Column-I Column-II
I) $F$ A) $(m_{1} + m_{2}) g$
II) Force acting on $m_{2}$ is B) $m_{2} g \sec θ$
III) Tension in the string is C) $m_{2} \frac{F}{m_{1} + m_{2}}$
IV) Force acting on $m_{1}$ by the wire is D) $(m_{1} + m_{2}) g \tan θ$

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$I \to D, I I \to A, I I I \to C, I V \to B$

$I \to D, I I \to C, I I I \to B, I V \to A$

$I \to D, I I \to B, I I I \to C, I V \to A$

$I \to A, I I \to C, I I I \to D, I V \to B$

answer is B.

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Detailed Solution

Question Image

$\to F = (m_{1} + m_{2}) a$
$T \sin θ = m_{2} a$
$T = m_{2} g \sec θ$
Solving above equations
$a = g \tan θ$
So, $\Rightarrow F = (m_{1} + m_{2}) g \tan θ$
$\Rightarrow$ Net force on $m_{2}$
is $= \frac{m_{2} F}{m_{1} + m_{2}} \Rightarrow$ Force on $\Rightarrow m_{1}$
$N = m_{1} g + T \cos θ = (m_{1} + m_{2}) g$
And tension, $T = m_{2} g \sec θ$

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