A mass of 10 k g is suspended by a rope of length 4 m , from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45 ° with the vertical. Then F equals: (Take g = 10 m s - 2 and the rope to be massless)

Question

A mass of 10 k g is suspended by a rope of length 4 m , from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45 ° with the vertical. Then F equals: (Take g = 10 m s - 2 and the rope to be massless), 100 N, 90 N, 70 N, 75 N

MARKS App · Accepted Answer

Let the tension in the string is T . Applying the condition of equilibrium in the vertical direction, T cos 45 ° = 100 ⇒ T 2 = 100 . . . 1 In the horizontal direction, T sin 45 ° = F ⇒ T 2 = F Put the value of T from equation 1 , ⇒ F = 100 N So, the horizontal force applied on the rope will be 100 N .

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