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In the figure shown, `AB = BC = 2m`. Friction coefficient everywhere is `mu=0.2.` Find the maximum compression of the spring.

Answer

B, D

Explanation

Let x be the maximum extension.
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`h = (2+x) sin 30^(@) = (1+0.5x)m`
The block has travelled `d_(1) =2m` on rough horizontal ground and `d_(2)=(2+x)m` on rough inclined ground . In the initial position block has only kinetic enetgy and in the final position spring and gravitational potential energy. so, applying the equation.
`E_(i)-E_(f) =` work done against friction
`rArr ((1)/(2)mv^(2))-((1)/(2)kx^(2) + mgh) = mu mg d_(1) + (mu mg cos theta) d_(2)`
`rArr 1/2 xx 2 xx (10)^(2)-1/2 xx x^(2) -2xx10xx(1+0.5x) = 0.2xx2xx10xx2 + (0.2xx2xx10xxcos 30^@)(2+x)`
Solving this equation we get,
`x=2.45m`.