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A block of mass m is connected to a peg at point D through a light and inextensible string of length 18 m. The length of section AB is 3 m. The point C of string is pulled down by applying a force F of 128 N. Block A remains stationary. If the mass of block,4 is 16n kg, the value of n is  __________.

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answer is 2.

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Detailed Solution

From the figure,    EC=(7.5)2−(4.5)2=6m    sin⁡θ=4.57.5=35⇒cos⁡θ=6.07.5=45    2F′cos⁡θ=128⇒     2F′×45=128⇒F′=128×58=80N For block at A,F′=mgsin⁡45∘    80=m×10×12⇒m=82kg∴     16n=82 Or      n=1682=2∴     n=2
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