Three uniform objects having the same mass and diameter are released simultaneou

Question

Three uniform objects having the same mass and diameter are released simultaneously from rest at the same distance above the bottom of a hill and roll down without slipping. The objects are a solid sphere, a solid cylinder, and a thin-walled hollow cylinder. Which of these objects will be the first one to reach the bottom of the hill? solid sphere solid cylinder thin-walled hollow cylinder all reach bottom at same time Three uniform objects having the same mass and diameter are released simultaneously from rest at the same distance above the bottom of a hill and roll down without slipping. The objects are a solid sphere, a solid cylinder, and a thin-walled hollow cylinder. Which of these objects will have the greatest kinetic energy at the bottom of the hill? solid sphere solid cylinder thin-walled hollow cylinder all have same kinetic energy at bottom Three uniform objects having the same mass and diameter are released simultaneously from rest at the same distance above the bottom of a hill and slide down without rolling. The objects are a solid sphere, a solid cylinder, and a thin-walled hollow cylinder. Which of these objects will be the first one to reach the bottom o the hill? solid sphere solid cylinder thin-walled hollow cylinder all reach bottom at same time A block moving to the right on a frictionless floor collides with a block moving to the left. The two block stick together and move off as a unit. The total kinetic energy of the system after the collision: is smaller than the total kinetic energy before the collision. is equal to the kinetic energy before the collision. is greater than the total kinetic energy before the collision. is zero. cannot be determined without knowing the speeds of the two blocks

Explanation / Answer

1) by energy conservation,

PE = KE

mgh = 0.5 mv^2 + 0.5 i w^2

Since v =wr

For hollow cylinder, KE =0.5 mv^2 + 0.5 mr^2 w^2 = mv^2

Similarly For solid cylinder, KE = 0.75 mv^2

Similarly For solid sphere KE = 0.7 mv^2

We can see that velocity in the case of solid sphere is maximum.

Hence solid sphere will reach first.

2) all will have same KE by energy conservation

3) by energy conservation,

PE = KE

mgh = 0.5 mv^2 as here is no rolling

For all bodies , KE =0.5 mv^2, So v is same.

Hence all will reach at same time

4) because energy will be lost in collision as it is inelastic collision.

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