A block of mass m1 rests on a horizontal table. A string tied to this block is passed over a frictional pulley fixed at one end of the table and another block of mass m2 is hung to the other end of the string. The acceleration (a) of the system is :

Question

A block of mass m1 rests on a horizontal table. A string tied to this block is passed over a frictional pulley fixed at one end of the table and another block of mass m2 is hung to the other end of the string. The acceleration (a) of the system is : (A)  (m1m2g/m1-m2)  (B)  (m2g/m1+m2)  (C)  (m1g/m1+m2)  (D)  g

Tardigrade Admin · Accepted Answer

Force acting on block which causes acceleration is

F = ma

.
The free body diagram depicting the situation is shown.

Resultant force acting on hanging block is

(m_{2} g - T)

.
Force acting on block

m_{2}

which causes acceleration is

m_{2} a

Hence,

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

... (i)
Also,

T = m_{1} a

... (ii)
From Eqs. (i) and (ii), we get

a = \frac{m _{2} g}{m _{1} + m _{2}}

Q. A block of mass $m_{1}$ rests on a horizontal table. A string tied to this block is passed over a frictional pulley fixed at one end of the table and another block of mass $m_{2}$ is hung to the other end of the string. The acceleration $(a)$ of the system is :

$\frac{m _{1} m _{2} g}{m _{1} - m _{2}}$

$\frac{m _{2} g}{m _{1} + m _{2}}$

$\frac{m _{1} g}{m _{1} + m _{2}}$

$g$

Q. A block of mass m1​ rests on a horizontal table. A string tied to this block is passed over a frictional pulley fixed at one end of the table and another block of mass m2​ is hung to the other end of the string. The acceleration (a) of the system is :

m1​−m2​m1​m2​g​

m1​+m2​m2​g​

m1​+m2​m1​g​

g

Q. A block of mass $m_{1}$ rests on a horizontal table. A string tied to this block is passed over a frictional pulley fixed at one end of the table and another block of mass $m_{2}$ is hung to the other end of the string. The acceleration $(a)$ of the system is :

$\frac{m _{1} m _{2} g}{m _{1} - m _{2}}$

$\frac{m _{2} g}{m _{1} + m _{2}}$

$\frac{m _{1} g}{m _{1} + m _{2}}$

$g$