Question

Two unequal masses m, and m, are connected
by a string going over a clamped light smooth
pulley as shown in figure. m1= 3 kg and m2 = 6
kg. The system is released from rest. (a) Find
the distance travelled by the first block in the
first two seconds. (b) Find the tension in the
string. (c) Find the force exerted by the clamp
on the pulley. (g = 10 m/s)​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Distance\:travelled=\frac{20}{3}\:m}}}$

$\green{\tt{\therefore{Tension\:in\:string=40\:N}}}$

$\green{\tt{\therefore{Force\:exerted\:by\:clamp\:on\:pulley=80\:N}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies m_{1} = 3 \: kg \\ \\ \tt: \implies m_{2} = 6 \: kg \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Distance \: travelled \: by \: first \: block \: in \: first \: two \: second= ? \\ \\ \tt: \implies Tension \: in \: the \: string = ? \\ \\ \tt: \implies Force \: exerted \: by \: the \: clamp \: on \: the \: pulley = ?$

• According to given question :

$\bold{For \: finding \: distance \: travelled} \\ \tt: \implies m_{2} g - T= m_{2}a - - - - - (1) \\ \\ \tt: \implies T - m_{1}g = m_{1}a - - - - - (2) \\ \\ \circ \: \text{Adding \: (1) \: and \: (2)} \\ \tt: \implies m_{2}g - m_{1}g = (m_{1} + m_{2})a \\ \\ \tt: \implies a = \frac{(m_{2}- m_{1})g}{ m_{1} + m_{2} } \\ \\ \text{Putting \: given \: values} \\ \tt: \implies a = \frac{6 - 3}{3+6} \times 10 \\ \\ \tt: \implies a = \frac{10}{3} \:m/{s}^{2} \\ \\ \bold{From \: second \: eqn \: of \: motion} \\ \tt: \implies s = ut + \frac{1}{2} a {t}^{2} \\ \\ \tt: \implies s = 0 \times 2 + \frac{1}{2} \times \frac{10}{3} \times 2^{2} \\ \\ \green{\tt: \implies s = \frac{20}{3} \: m} \\ \\ \bold{For \: Tension \: in \: the \: string} \\ \tt: \implies T- m_{1}g = m_{1}a \\ \\ \tt: \implies T - 3 \times 10 = 3 \times \frac{10}{3} \\ \\ \tt: \implies T= 10 + 30 \\ \\ \green{\tt: \implies T = 40 \: N}\\ \\ \bold{Force \: exerted \: by \: clamp \: on \: pulley}\\ \tt: \implies Force = 2T \\ \\ \tt: \implies Force = 2 \times 40 \\ \\ \green{\tt: \implies Force = 80 \: N}$