A block of mass m is attached to one end...

A block of mass m is attached to one end of a mass less spring of spring constant k. the other end of spring is fixed to a wall the block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is `mu` then the compession of the spring for which maximum extension of the spring becomes half of maximum compression is .

`(2mg mu)/(k)`

`(mg mu)/(k)`

`(4mg mu)/(k)`

None of these

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The correct Answer is:

`E_(i)-E_(f) =` Work done againt fricion
`:. 1/2kx^(2)-1/2K(x/2)^(2) =mu mg (x+x/2)`
`:. x=(4mu mg)/k`.

A block of mass m is moving with a speed v on a horizontal rought surface and collides with a horizontal monted spring of spring constant k as shown in the figure .The coefficient of friction between the block and the floor is mu The maximum cobnpression of the spring is

`- (mu mg)/(k) + (1)/(k) sqrt((mu mg)^(2) + mkv^(2))`

` (mu mg)/(k) + (1)/(k) sqrt((mu mg)^(2) + mkv^(2))`

`- (mu mg)/(k) + (1)/(k) sqrt((mu mg)^(2) - mkv^(2))`

`(mu mg)/(k) + (1)/(k) sqrt((mu mg)^(2) + mkv^(2))`

`(1)/(4)sqrt((mv^(2))/(k))`

`sqrt((mv^(2))/(k))`

`(1)/(2)sqrt((mv^(2))/(k))`

`2sqrt((mv^(2))/(k))`

The spring was initially compessed by a distance x and was finally in its natural length .

It was initially stretched by a distance x and finally was in its natural length.

It was initially natural length and finally in a compressed position.

It was initially in its natural length and finally in a stretched position.