A dumbbell consists of two masses m and 2m separate by a distance d by a massles

Question

A dumbbell consists of two masses m and 2m separate by a distance d by a massless rod. The dumbbell rests on a frictionless horizontal table, and a force F is pulling mass m to the right. In the figure we are looking down at the dumbbell from above Are there one or more forces that can be applied to the dumbbell that will cause it to move with only translational motion, without any rotation? If yes what is/are those forces, magnitude, direction, and applied to what part of the dumbbell? If not, explain. In addition to the force shown in the figure are there one or more forces that can be applied to the dumbbell that will cause it to move with only constant translational speed, without any rotation or acceleration? If yes what is/are those forces, magnitude, direction, and applied to what part of the dumbbell? If not, explain.

Explanation / Answer

A.) yes,

force would be 2F in the same direction parallel to F but point out from mass 2m

as net torque become zero so body will not have rotational movement but have only translational movement

B.)yes,

force would be F in the opposite to the direction of F and parallel to F point out from mass m .

as net Force and torque become zero so it will move with constant velocity without any rotation.

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