Match the column-I to value of Tension in column-Il assuming mass of particle equal to m
Column-I Column-II
(a)
Extreme position in simple pendulum
(p) $\frac{4 mg}{5}$
(b)
Conical pendulum
(q) $\frac{5 mg}{4}$
(c)
Cart is accelerated such that particle remains at rest as shown w.r.t. cart.
(r) $\frac{3 mg}{5}$
(d)
Cart is accelerating freely on the incline. Particle remains at rest w.r.t. cart as shown.
(s) $\frac{5 mg}{3}$

Moderate

Solution

(a) As velocity = 0
   $\Rightarrow$ No radial acceleration
$\begin{matrix} \Rightarrow T = mgcos 53^{\circ} \\ = \frac{3 mg}{5} \end{matrix}$
(b) Motion in horizontal plane
$\Rightarrow$ no acceleration in vertical direction
   $\begin{array}{l} \Rightarrow Tcos 37^{\circ} = mg \\ \Rightarrow T = \frac{mg \times 5}{4} \end{array}$
(c) Acceleration of particle w.r.t. cart is zero
   $\begin{array}{l} \Rightarrow Tcos 53^{\circ} = mg \\ \Rightarrow T = \frac{5 mg}{3} \end{array}$
(d) $T = mgcos 37^{\circ}$
$\Rightarrow T = \frac{4 mg}{5}$

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Column-I		Column-II
(a)	Extreme position in simple pendulum	(p)	$\frac{4 mg}{5}$
(b)	Conical pendulum	(q)	$\frac{5 mg}{4}$
(c)	Cart is accelerated such that particle remains at rest as shown w.r.t. cart.	(r)	$\frac{3 mg}{5}$
(d)	Cart is accelerating freely on the incline. Particle remains at rest w.r.t. cart as shown.	(s)	$\frac{5 mg}{3}$