Question

Two masses of \[4kg\] and \[5kg\] are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in figure .The acceleration of \[5kg\] mass is.

Answer 1

Hint: A pulley is a wheel on an axle or shaft that is designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. Pulleys are assembled to form a block and tackle in order to provide mechanical advantage to apply large forces.

Complete step by step solution:
What we mean by a frictionless pulley is that the friction in the bearings of the pulley is negligible, and the pulley is free to rotate without any resistance. We don't mean that the friction between the string and the pulley surface is negligible.
Here, the same tension force is present as there is only on \[5kg\] string used in this system. Also, the acceleration of the system is \[a\] which acts in the downward direction as the mass \[5kg\] is greater than the other mass of \[4kg\]. According to this the free body diagram will be:

We are given the following things,
\[{M_1} = 4kg\]
\[{M_2} = 5kg\]
The equation of force on ${M_1}$,
$T = 4a.......(1)$
The equation of force on ${M_2}$,
$5g - T = 5a........(2)$
On putting the value of tension $T$ from equation (1) in equation (2),
$5g - 4a = 5a$
$5g = 4a + 5a$
$9a = 5g$
On taking $9$ on the other side, we get,
$a = \dfrac{{5g}}{9}$
On putting $g = 9.8\dfrac{m}{{{s^2}}}$, we get,
$a = \dfrac{{5 \times 9.8}}{9}$
\[a = \dfrac{{49}}{9}\]
\[a = 5.44\dfrac{m}{{{s^2}}}\]
So, the final answer is \[a = 5.44\dfrac{m}{{{s^2}}}\]

Note: It is important to note that in this question, we are given a frictionless surface so that the problem does not get complicated and so that the question can easily be solved. But in real practical life, a proper frictionless surface does not exist. If there was no friction everything would slide to the lowest point.