A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2 \mathrm{~m} / \mathrm{s}^{2}$. The normal reaction $\mathrm{R}^{\prime}$ by the floor if mass of the iron cylinders are equal and of 20 kg each, is \_\_\_\_ N. [ Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and $\mu_{\mathrm{s}}=0.2$ ]

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Laws of Motion

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration

0.2 m / s^{2}

. The normal reaction

R^{'}

by the floor if mass of the iron cylinders are equal and of 20 kg each, is ____ N.
[ Take

g = 10 m / s^{2}

and

μ_{s} = 0.2

]

(A)714
(B)684
(C)716
(D)686✓ Correct

Answer: (D)

Solution

The block and the three cylinders descend together, so the mass carried by the floor is

m = 10 + 3 \times 20 = 70

kg. Taking the downward direction as positive and writing Newton's second law for the whole assembly,

m g - R^{'} = ma

R^{'} = m (g - a) = 70 (10 - 0.2) = 686 N

The floor pushes up on the assembly with

686

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option

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