A block of mass 200 kg is being pulled up by men on an inclined plane at an angle of `45^@` as shown. The coefficient of static friction is 0.5. Each man can only apply a maximum force of 500 N. The number of men required for the block to just start moving up the plane is

Options

A. 10
B. 15
C. 5
D. 3

Answer

C

Explanation

here , mass of the block `m = 200 kg `
coefficient of static friction ` mu_s = 0.5 =1/2`
angle of incline plane `, theta = 45^@`
maximum force that each man can apply `F= 500 N`
Let N number of men be requied for the block to just start moving up to the plane . Then
` NF = mg sin theta + f = mg sin theta + mu_s R`
` = mg sin theta + mu_s mg cos theta = mg [ sin theta + mu_s cos theta ]`
` = 200 xx 10 [ sin 45^@ +1/2 cos 45^@]`
` = 200 xx 10 [ (1)/( sqrt(2))+(1)/( 2sqrt(2)] = ( 200 xx 10 xx 3)/( 2 sqrt(2))`
`or N=( 200 xx 10 xx 3 )/( 2 sqrt(2) xx 500)~~5`