A body is sliding down a rough inclined plane The coefficient of friction between the body and the plane is `0.5`.The ratio of the net force required for the body to slide down and the normal reaction on the body is `1:2` Then the angle of the inclined plane is

Options

A. `15^@`
B. `30^@`
C. `45^@`
D. `60^@`

Answer

C

Explanation

Here ` mu = 0.5 , (F_("net"))/( N )=1/2`
Let ` theta ` be the angle of incclined plane , then
` F_("net") =mg sin theta - f `
As ` f = mu N and N = mg cos theta `
` therefore F_(" net") = mg sin theta - mu mg cos theta `
` therefore (F_("net") )/( N ) = ( mg sin theta - mu mg cos theta )/( mg cos theta) = 1/2`
` or tan theta - 0.5 = 1/2 or tan theta = 1 or theta = 45^@`
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