A particle of mass m = 1 kg is dropped from a height h = 40 cm on a light horizontal platform fixed to one end of an elastic spring, the other being fixed to a base, as shown in the diagram. The particle collides with the platform and sticks to it. As a result, the spring is compressed by an amount x = 10 cm . What is the force constant of the spring? (Take g = 10 m s - 2 )

Question

A particle of mass m = 1 kg is dropped from a height h = 40 cm on a light horizontal platform fixed to one end of an elastic spring, the other being fixed to a base, as shown in the diagram. The particle collides with the platform and sticks to it. As a result, the spring is compressed by an amount x = 10 cm . What is the force constant of the spring? (Take g = 10 m s - 2 ), 600 N m - 1, 800 N m - 1, 1000 N m - 1, 1200 N m - 1

MARKS App · Accepted Answer

Since the platform is depressed by an amount x, the total work done on the spring is m g ( h + x ) . This work is stored in the spring in the form of potential energy 1 2 k x 2 . Equating the two, we have 1 2 k x 2 = m g h + x or k = 2 mg h + x x 2 Given, h = 0 . 4 m , x = 0 . 1 m , m = 1 kg and g = 10 m s - 2 . Substituting these values, we get k = 1000 N m - 1 .

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