A block of mass $1 k g$ moves 2 m towards a spring of force constant $10 N / m$ and then comes in contact with it . The spring is massless and unstretched. The coefficient of friction between block and surface is $0.30$ . After compressing the spring, block does not return back: $(g = 10 m / s)$

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the maximum value of speed of block for which it is possible is $3.8 m / s$

statement in option (3) is wrong

the maximum value of speed of block for which it is possible is $4.2 m / s$

if $E_{i}$ and $E_{f}$ are initial and final mechanical energy, which is sum of kinetic energy and potential energy, then work done by friction on a system is $(E_{i} - E_{f})$

answer is A, C.

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Detailed Solution

The spring is compressed by $x$

Block will not return if $μ m g \geq K x$

So, $x_{m a x} = \frac{μ m g}{K} = \frac{(0.3) (1) (10)}{10} = 0.30 m$

work done against friction $= E_{i} - E_{f}$

$μ m g (x + 2) = \frac{1}{2} m v_{0}^{2} - \frac{1}{2} K x^{2} (0.3) (1) (10) (0.3 + 2) = (\frac{1}{2}) (1) v_{0}^{2} - (\frac{1}{2}) (10) {(0.3)}^{2}$