Question

Two blocks of identical mass are connected by a light string as shown below. The surface is frictionless and the pulley is massless and frictionless. The acceleration of the two block system is most nearly

Answer 1

Hint: To solve this question, first find the tension in the string connected to block 1. Then, find the tension in the string connected to block 2. Compare these two obtained equations. Now, evaluate the obtained expression and cancel out the common terms and obtain an expression for acceleration in terms of g which is acceleration due to gravity. We know, $g=10{m}/{s}$, substitute this value in the expression for acceleration. This will give the acceleration of the two block system.

Complete answer:

Let the mass of both the blocks be m
Tension in the string connected to block 1 is given by,
$T= ma$ …(1)
Tension in the string connected to block 2 is given by,
$mg-T= ma$
$\Rightarrow T= mg-ma$ …(2)
Comparing equation. (1) and (2) we get.
$ma=mg-ma$
$\Rightarrow ma+ma=mg$
$\Rightarrow mg= 2ma$
Cancelling the common terms on both the sides we get,
$g=2a$
$\Rightarrow a= \dfrac {g}{2}$
We know, $g=10{m}/{s}$
Substituting value of g in above equation we get,
$a=\dfrac {10}{2}$
$\Rightarrow a=5$
Thus, the acceleration of the two block system is almost $5{m}/{s}$.

Note:
Students usually get confused between stress and tension. They should remember that the tension is the force acting along the length when an object is pulled from both sides. Whereas stress the effect of force acting on the object. The tension is one of the forces which is produced when mass is attached to a string under gravitational force. S.I unit of tension is the same as that of force which Newton denoted by N.