Question

Consider the situation shown in fig. Both the pulleys and the string are light and all the surfaces are frictionless.
(a) Find the acceleration of the mass M.
(b) Find the tension in the string.
(c) Calculate the force exerted by the clamp on the pulley A in the figure.

Answer 1

By constrain relation

$-T{a}_1+2T{a}_2=0$

$2a_2=a_1$ ........(1)

$Mg-T=m{a}_1$ .........(2)

$2T=2m{a}_2$

$T=\frac{m{a}_1}{2}$

$m{a}_1=2T$ ........(3)

Adding (2) + (3)

$mg-\frac{m{a}_1}{2}=m{a}_1$

$g=\frac{3}{2}{a}_1$

$a_1=\frac{2}{3}g$

$T=\frac{m\times 2g}{3\times 2}=\frac{mg}{3}$

$N=2Tcos{45}^{\circ }$

$=2\times T\times \frac{1}{\sqrt{2}}$

$=\frac{mg}{3\sqrt{2}}$