A piece of sheet metal of mass M is cut into the shape of a right triangle. A ve

Question

A piece of sheet metal of mass M is cut into the shape of a right triangle. A vertical dasshed line is drawn on the sheet at the point where the mass to the left of the line (M/2) is equal to the mass to the right of the line (also M/2). The sheet is now placed on a fulcrum just under the dashed line and released from rest.
(a) Does the metal sheet remain level, tip to the left, or tip to the right? (b) Choose the best explanation from among the following.

I. equal mass on either side will keep the metal sheet level
II. the metal sheet extends for a greater distance to the left which shifts the center of mass to the left of the dashed line
III. the center of mass is to the right of the dashed line because the metal sheet is thicker there

Explanation / Answer

metal sheet remains level if : the perpendicular distance of center of mass of one side of triangle from the vertical line equals the perpendicular distance of center of mass of other side of triangle from the vertical line. then as two masses are equal torques exerted by both halves balance each other; torque = perpendicular distance of center of mass of side of triangle from the vertical line * m/2. shifts to the left if the length of triangle on left side is larger than the length of other side. because distance of center of mass of left half would be greater than distance of center of mass of right causing the torque by left to be greater than torque by right shifts to the right under vice versa condition therefore II is the possible explanation as the triangle is right angled density to the right is high doesn't mean the position of center of mass of right is at greater distance from that of left

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