Question

A light string passes over a frictionless pulley. To one of its ends a mass of $8kg$ is attached. To its other end two masses of $7kg$ each are attached. The acceleration of the system will be:

A. $10.2g$
B. $5.10g$
C. $20.36g$
D. $0.27g$

Answer 1

Before going through the question let us first know about pulley. It is a simple metal or wood machine with a wheel and a seam to lift heavy loads. Nowadays, plastic pulleys are also available in the market to carry small loads. This can be rotated freely through the centre of an axis. It can change the direction of a force making lifting anything much easier.

Complete step by step answer:
What we mean by a friction less is that it is negligible to rotate without any resistance to the friction in the pulley's coils. The friction is not insignificant between the string and the pulley surface. Now, let us solve the given question;

From the free body diagram of body A
${m_1}a = {T_1} - {m_1}g\,\,\,......\left( i \right)$
Similarly, from the free body diagram of body B
${m_2}a = {m_2}g + {T_2} - {T_1}\,\,......\left( {ii} \right)$
Again, from the free body diagram of body C
${m_3}a = {m_3}g - {T_2}\,.......\left( {iii} \right)$
On solving the equations (i), (ii) and (iii), we get
$a = \dfrac{{\left[ {\left( {{m_2} + {m_3}} \right) - {m_1}} \right]g}}{{{m_1} + {m_2} + {m_3}}}$
As, ${m_1} = 8kg,\,{m_2} = {m_3} = 7kg$
$a = \dfrac{6}{{22}}g \\\ \therefore a= 0.27g$
Therefore, the acceleration of the system will be $0.27g$.

Hence, the correct option is D.

Note: Pulleys are used to adjust the speed, rotation direction or torque or torque. A pulley system has two pulley wheels connected by a belt, each one on a shaft. This conveys rotary movement and power from the input or control shaft to the output or controlled shaft.