A solid small sphere of radius 4.5 cm and weight W, is to be suspended by a string from the ends of a smooth hemispherical bowl of radius 49 cm. It is found that if the string is any shorter than 40 c

Question

A solid small sphere of radius 4.5 cm and weight W, is to be suspended by a string from the ends of a smooth hemispherical bowl of radius 49 cm. It is found that if the string is any shorter than 40 cm, it breaks. What is the breaking strength of the string is F = ( p /10 )

TestHub · Accepted Answer

Geometry: OP = 49 cm, O O ′ = 49 − 4.5 = 44.5 cm, and with the 40 cm string P O ′ = 40 + 4.5 = 44.5 cm The triangle is isoceles, so tension and normal are symmetric: each makes angle θ with the vertical, cos θ = 44.5 44. 5 2 − 24. 5 2 ​ ​ = 0.835 Horizontal balance gives N = T ; vertical balance: 2 T cos θ = W T = 2 × 0.835 W ​ = 0.6 W = 10 6 ​ W , so p = 6

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