1
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Question

# Three equal masses of 1 kg each are placed at the vertices of an equilateral triangle PQR and a mass of 2 kg is placed at the centroid O of the triangle which is at a distance of √2 m from each of the vertices of the triangle. The net force (in Newton), acting on the mass of 2 kg is

A
2
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B
2
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C
1
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D
zero
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Solution

## The correct option is D zeroGiven: OP=OQ=OR=√2 m m=1 kg; M=2 kg The gravitational force on mass 2 kg due to mass 1 kg at P. FOP=G2×1(√2)2=G along OP Similarly, FOQ=G2×1(√2)2=G along OQ FOR=G2×1(√2)2=G along OR Net force at O in direction parallel to the base of triangle is due to force FOQ and FOR . FOQcos30∘ and FORcos30∘ are equal and acting in opposite directions, thus balance each other. Therefore net force at O will be in vertical direction. The resultant force on the mass 2 kg at O is given by Fnet=FOP−(FOQsin30∘+FORsin30∘) ⇒Fnet=G−(G2+G2)=0 Hence, option (d) is correct. Why this question: To help students understand the Principle of Superposition. Key Concept: Principle of Superposition - The gravitational force between two masses is independent of other masses in the vicinity and the net force on a mass is equal to the vector sum of forces by all the masses.

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