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Q.

A block of mass 'm' is attached with a massless spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is $μ = \frac{3}{4}$ . The minimum value of M required to move the block up the plane is (Neglect mass of pulley, string and friction in pulley.)

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a

6/5 m

b

3/5 m

c

4/5 m

d

3/2 m

answer is A.

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Detailed Solution

Question Image

$f_{max} = μ N = μ mg \cos θ$

$μ mg \cos 37 ° = \frac{3}{4} mg (\frac{4}{5})$

$f_{max} = \frac{3}{5} mg from fig$

$mg sin θ = mg sin37° = mg (\frac{3}{5})$

When block will move upwards when

$K x_{0} = mg \sin θ + f_{max} = \frac{3}{5} mg + \frac{3}{5} mg$

$K x_{0} = \frac{6}{5} mg$

From conservation of mechanical energy

$Mg x_{0} = \frac{1}{2} K x_{0}^{2}$

$M = \frac{K x_{0}}{2 g} = \frac{\frac{6}{5} mg}{2g}$

$∴ M = \frac{3}{5} m$

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