The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, while door B rotates about an axis through the center. The same fo

Question

The drawing shows the top view of two doors. The doors are uniform and identical. Door A rotates about an axis through its left edge, while door B rotates about an axis through the center. The same force F is applied perpendicular to each door at its right edge and the force remains perpendicular as the door turns. Starting from rest, door A rotates through a certain angle in 3 s . If door B takes $\frac{3 n}{2} sec$ to rotate through the same angle. Fill the value of 'n' in OMR sheet.

CT43 n4 diagram

TestHub · Accepted Answer

Door A has torque FL and moment ML²/3, so αA=3F/(ML).

Door B has torque FL/2 and moment ML²/12, so αB=6F/(ML)=2αA.

For equal angles from rest, time is proportional to 1/√α; hence tB=3/√2.

Since tB=3n/√2, n=1.

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