Question

Two bodies A and B are attached to the end of a string which passes over
a pulley, so that they hang vertically. If the mass of the body B is 4 kg;
find mass of the body A which moves up with an acceleration of 0.5 ms^2
(Take g = 10 ms)

Answer 1

Given:

Two bodies A and B are attached to the end of a string which passes over a pulley, so that they hang vertically. The mass of the body B is 4 kg.

To find:

Mass of body A if net acceleration of system is 0.5 m/s².

Diagram:

$\setlength{\unitlength}{2mm}\begin{picture}(0,0)\linethickness{0.4mm}\put(0,0){\line(3,0){4cm}}\put(10,0){\line(0,-3){0.8cm}}\put(10,-7.2){\thicklines\circle{6}}\multiput(6.9,-8)(6.2,0){2}{\line(0,-3){2cm}}\put(6.9,-16){\line(0,-3){1cm}}\put(5.2,-22.3){\boxed{\Huge\sf m}}\put(11.5,-19.3){\boxed{\Huge\sf 4 kg}}\multiput(1,0)(1,0){19}{\qbezier(0,0)(0.4,0.4)(0.9,0.9)}\end{picture}$

Calculation:

According to FBD of 4 kg block:

$\therefore \: 4g - T = 4a$

$\implies \: 40 - T = 4(0.5)$

$\implies \: 40 - T = 2$

$\implies \: T = 38 \: N$

According to FBD of m_(A) block :

$\therefore \: T - mg = ma$

$\implies \: 38 - 10m = m(0.5)$

$\implies \: 38 = 10.5(m)$

$\implies \: m = 3.61 \: kg$

So, mass of block A is 3.61 kg.

Answer 2

Answer:

Two bodies A and B are attached to the end of a string which passes over a pulley, so that they hang vertically. The mass of the body B is 4 kg.