JEE Main 2022 — Laws Of Motion Question with Solution

The vertical component of the tension, $$T\cos \theta$$, balances the weight of the mass:

$$T\cos \theta =mg$$

Since $$mg=10\text{ kg}\times 10{\text{ m/s}}^2=100\text{ N}$$:

$$T\cos \theta =100\text{N}$$ ...... (i)

The horizontal component of the tension is given by:

$$T\sin \theta =30\text{N}$$ ........ (ii)

Dividing equation (ii) by equation (i):

$$\frac{T\sin \theta }{T\cos \theta }=\frac{30}{100}$$

Therefore:

$$\tan \theta =\frac{3}{10}$$

Hence, the value of x is:

$$\therefore x=3$$