A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g / 8, then the ratio of the masses is :

Question

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g / 8, then the ratio of the masses is : (A) 8: 1 (B) 9: 7 (C) 4: 3 (D) 5: 3

Tardigrade Admin · Accepted Answer

As the string is inextensible, both masses have the same acceleration

a

. Also, the pulley is massless and frictionless, hence, the tension at both ends of the string is the same. Suppose the mass

m_{2}

is greater than mass

m_{1},

so, the heavier mass

m_{2}

is accelerated downward and the lighter mass

m_{1}

is accelerated upwards.

Therefore, by Newton's 2 nd law

T - m_{1} g = m_{1} a

...(1)

m_{2} g - T = m_{2} a

...(2)
After solving Eqs. (1) and (2)

a = \frac{( m _{2} - m _{1} )}{( m _{1} + m _{2} )} \cdot g = \frac{g}{8}

(given)
so,

\frac{g}{8} = \frac{m _{2} ( 1 - m _{1} / m _{2} )}{m _{2} ( 1 + m _{1} / m _{2} )} \cdot g

Let

\frac{m _{1}}{m _{2}} = x

Thus Eq. (3) becomes

\frac{1 - x}{1 + x} = \frac{1}{8}

or

x = \frac{7}{9}

or

\frac{m _{2}}{m _{1}} = \frac{9}{7}

So, the ratio of the masses is 9: 7 .

Q. A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (vertically). If the acceleration of the system is $g /8$ , then the ratio of the masses is :

8 : 1

9 : 7

4 : 3

5 : 3

Q. A light string passing over a smooth light pulley connects two blocks of masses m1​ and m2​ (vertically). If the acceleration of the system is g/8, then the ratio of the masses is :

8 : 1

9 : 7

4 : 3

5 : 3

Q. A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (vertically). If the acceleration of the system is $g /8$ , then the ratio of the masses is :