Question

A particle is suspended from a string of length$R$. It is given a velocity $u=3\sqrt{gR}$ at the bottom.
Match the following columns.

Column-I	Column-II
(a)	Velocity at B	(p)	7 mg
(b)	Velocity of C	(q)	$\sqrt{5gR}$
(c)	Tension in string at B	(r)	$\sqrt{7gR}$
(d)	Tension in string at C	(s)	5 mg
		(t)	None

• A. a-r, b-q, c-p, d-s
• B. a-r, b-p, c-s, d-p
• C. a-r, b-p, c-p, d-t
• D. a-r, b-q, c-p, d-t

Answer 1

The correct option is D a-r, b-q, c-p, d-t

$(A\to r,B\to q,C\to p,D\to t)$
$v_B^2-v_A^2=-2g{h}_{AB}\Rightarrow v_B^2=\left(9gR\right)-\left(2gR\right)=7gR$
$\therefore v_B=\sqrt{7gR}$
Further, $T_B=\frac{m{v}_B^2}{R}=7mg$
Again, $[v_C^2=v_A^2-2g{h}_{AC}$
$=\left(9gR\right)-2\left(2R\right)=5gR]$
$\therefore v_C=\sqrt{5gR}$
Further, $T_C+mg=\frac{m{v}_C^2}{R}$
$\therefore T_C=4mg$