JEE Physics 2023 Question with Solution

Step-by-step solution

Standard Method

Given: mass of the roller is $m = 70 \, \text{kg}$, applied force is $F = 200 \, \text{N}$, angle with horizontal is $30^\circ$, and $g = 10 \, \text{m/s}^2$.

Find: the normal reaction $N$ on the roller.

The applied force has a downward vertical component, so it increases the normal reaction.

Using vertical force balance:

$$N = mg + F \sin 30^\circ$$

Now substitute the given values:

$$N = 70 \times 10 + 200 \times \frac{1}{2}$$ $$N = 700 + 100 = 800 \, \text{N}$$

Therefore, the normal reaction is $800 \, \text{N}$. The solution states the correct option is A, but this value corresponds to option C in the listed options.

Common mistakes

• Taking the vertical component of the applied force in the wrong direction. Here the force is directed downward, so $F \sin 30^\circ$ adds to $mg$. Do not subtract it from the normal reaction.

• Using $F \cos 30^\circ$ instead of $F \sin 30^\circ$ for the vertical component. Since the angle is given with the horizontal, the vertical component is $F \sin 30^\circ$.

• Choosing the option label directly from the page without checking the computed value. The working gives $800 \, \text{N}$, which matches option C, even though the solution labels the correct option as A.