As shown in figure, a 70 kg garden roller is pushed with a force of $\overrightarrow{\mathrm{F}}=200 \mathrm{~N}$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$)

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Laws of Motion

As shown in figure, a 70 kg garden roller is pushed with a force of

F = 200 N

at an angle of

3 0^{\circ}

with horizontal. The normal reaction on the roller is (Given

g = 10 m s^{- 2}

)

(A) $8002 N$
(B)600 N
(C)800 N✓ Correct
(D) $2003 N$

Answer: (C)

Solution

The applied force makes

3 0^{\circ}

with the horizontal and is directed downward into the roller, so it has a downward vertical component

F sin 3 0^{\circ} = 200 \times \frac{1}{2} = 100

N. Balancing forces in the vertical direction, the ground must support both the weight and this component,

N = m g + F sin 3 0^{\circ} = 70 \times 10 + 100 = 800

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Single correct option

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