Explanation Given Information: Mass of stone, m = 95 g = 95 × 10 − 3 kg Length of string, L = 85 cm = 85 × 10 − 2 m The time taken by stone to complete one revolution is 1.2 s . Formula used: According to Newton’s second law of motion: F = m a Where, F = Force m = Mass a = Acceleration Calculation: In horizontal circular motion centripetal force and force due to gravity is always mutually perpendicular. The following figure is used to solve: From figure the free body diagram(FBD) is made: From figure: m g = T sin θ .... ( 1 ) m v 2 r is a centripetal force and it is originated by the horizontal component of the tension. So, it should be equal to the horizontal component of the tension. m v 2 r = T cos θ .... ( 2 ) Dividing equation (1) and (2): tan θ = r g v 2 The velocity (v) is determined as follows: v = 2 π r t v = 2 π × L cos θ 1

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Chapter 5, Problem 75P

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The angle made by string with the horizontal.

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Chapter 5, Problem 74P

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The angle made by string with the horizontal.

Solution Summary: The following figure is used to solve Newton's second law of motion: a centripetal force and force due to gravity is always mutually perpendicular.

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