A block of mass 2 kg is attached with a horizontal spring of spring constant 260 N/m spring block system is initially compressed by 40 cm. When block is released it climbs up a rough inclined plane of inclination 53° as shown. If horizontal surface is smooth and coefficient of friction between block and incline is 0.4, the block rises on the incline up to a height of (g = 10 $m s^{- 2}$ )

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$\frac{4}{5} m$

$\frac{32}{25}$ m

$\frac{52}{35} m$

$\frac{52}{25} m$

answer is A.

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Detailed Solution

from conservation of energy $\frac{1}{2} k x^{2} = (m g \sin θ + μ m g \cos θ) l$

work done against frictional force and gravitaitonal force

$\frac{1}{2} 260 {(0.4)}^{2} = 20 (\frac{4}{5} + 0.4 \frac{3}{5}) l s o l v i n g f o r l = 1 m h = l \sin θ = \frac{4}{5} m$

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