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 `mu =3/4` find the minimum value of M required to move the block up the place. (Neglect mass of string and pulley. Ignore friction in pulley).
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Answer

C

Explanation

Let `X_(m)` is maximum extension of spring. Then decrease in potential energy of `M=` increase in elastic potential energy of spring`
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`:. 1/2kX_(m)^(2) =MgX_(m)`
or `X_(m) =(2Mg)/(k)`
Now, `kX_(m) =mg sin 37^@ + mumg cos 37^@`
or `2Mg = (mg) (3/5) +(3/4)mg(4/5)`
`:. M =3/5m`.