Question

Find tension in the thread as shown in diagram.

A) $12\,N$
B) $4\,N$
C) $0\,N$
D) $16\,N$

Answer 1

You can solve this question by first taking the components of the weight of the box or object which is on the slope, then finding the friction acting and then finding the difference between friction and the component of weight acting along the slope as the Tension of the string.

Complete step by step answer:
We will be proceeding with the solution exactly as told in the hint section of the solution to the question.
Firstly, let us assume the acceleration due to gravity as $10\,m{s^{ - 2}}$ to make our calculations easier.
Now, let’s find the weight of the block:
$W = mg = 2 \times 10 = 20\,N$
As the mass of the box is given as $2\,kg$
Now, we know that there are two components of the weight acting, one along the slope and another normal to the slope, which can be given as:
${W_{al}} = W\sin \theta$ (along the slope)
${W_n} = W\cos \theta$ (along the normal to the surface)
We know that
$\cos {37^ \circ } = \dfrac{4}{5} \\\ \sin {37^ \circ } = \dfrac{3}{5} \\\$
So, we substituting in the values, we get:
${W_{al}} = 12\,N \\\ {W_n} = 16\,N \\\$
We already know the formula of finding out the friction acting between a surface and an object as:
$f = {F_n} \times \mu$
We have already found out the value of the force acting along the normal to the surface, and the value of $\mu$ is given in the question as $0.75$
So, $f = 16 \times 0.75 = 12\,N$
Now, to find the net force acting on the box along the slope, we must add friction acting and the component of weight along the slope:
${F_{net}} = {W_{al}} + f$
We can clearly observe that the friction is acting upwards while the weight is acting downwards the slope, so:
${F_{net}} = 12 + \left( { - 12} \right) \\\ {F_{net}} = 0\,N \\\$
Since there is not net force acting on the box after the consideration of friction and weight, there is no need for tension in the string, that is:
$T = 0$

So, option (C) is the correct answer.

Note: Many students take the wrong components of weight along the slope and normal to the surface of the slope, and thus, get wrong results for the values of friction, and thus, tension in the string.