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A horizontal force F pulls a ring of mass m₁ such that $θ$ remains constant with time. The ring is constrained to move along a smooth rigid horizontal wire. A bob of mass m₂ hangs from m₁ by an inextensible light string. The match the entries of Column I with that of Column II.

Column - I
Column - II
A.
F P. $(m_{1} + m_{2}) g$
B.
Force acting on m₂ is Q. $m_{2} g \sec θ$
C.
Tension in the string is R. $\frac{m_{2} F}{m_{1} + m_{2}}$
D.
Force acting on $m_{1}$ by the wire is S. $(m_{1} + m_{2}) g t a n θ$

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$A - Q, B - R, C - S, D - P$

$A - R, B - P, C - Q, D - S$

$A - S, B - R, C - Q, D - P$

$A - S, B - R, C - P, D - Q$

answer is C.

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Detailed Solution

$T \cos θ = m_{2} g \Rightarrow T = m_{2} g \sec θ$

$F = (m_{1} + m_{2}) a, T \sin θ = m_{2} a$

$a = g T a n θ$

$F = (m_{1} + m_{2}) g \tan θ$

Net force on $m_{2} = m_{2} a = \frac{m_{2} F}{m_{1} + m_{2}}$

Force acting on m₁by wire $m_{2} g + T \cos θ = (m_{1} + m_{2}) g$

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