Question

In the situation given, the reading of the spring balance is ($g = 10m/{s^2}$).

A). $30N$
B). $33N$
C). $39N$
D). $40N$

Answer 1

In order to find the solution of the question, we need to draw a free body diagram of the above image including all the forces exerted on the body. Then we will find the tension in the spring balance to find the reading.

Complete step-by-step solution:

The free body diagram of the body is given as below:
The frictional force exerted by $2kg$ of body is
${f_1} = \mu {\rm N}$
${f_1} = \mu mg = 0.5 \times 2 \times 10 \\\ = 10N$
The frictional force exerted by $3kg$ body is
${f_2} = \mu {\rm N} \\\ \Rightarrow f_2^{} = \mu mg \\\ = 0.5 \times 3 \times 10 \\\ = 15N$
Then we need to find the acceleration find the tension between the spring:
${F_{net}} = ma \\\ \Rightarrow 60N + 10N - 15N - 15N = (3 + 2)a \\\ \Rightarrow 5a = 40 \\\ \Rightarrow a = 8m/{s^2}$
Now, we will find the tension in the wire of spring of the $2kg$body:
${T_1} + {f_1} - 15N = 2a \\\ \Rightarrow {T_1} + 10 - 15 = 2 \times 8 \\\ \Rightarrow {T_1} = 21N$
Now, we will find the tension in the wire of spring of the$3kg$body:
$60N - {T_2} - {f_2} = 3a \\\ \Rightarrow 60N - {T_2} - 15N = 24 \\\ \Rightarrow {T_2} = 19N$
Now the reading of spring balance will be:
$= {T_1} + {T_2} \\\ = 21N + 19N \\\ = 40N$
The reading in the spring balance in the above figure is $40N$.

Note: We need to keep some points in our mind while solving these problems:

The free body diagram is the most important thing in these kinds of questions so that we get to know the magnitude and direction of all the forces exerted.
We should have proper knowledge of laws of motion so that we can apply the accordingly.
We should remember all the required formulae.