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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A square plate of mass 120 ext g and edge 5.0 ext cm has a uniform...

A square plate of mass

120 ext{ g}

and edge

5.0 ext{ cm}

has a uniform angular acceleration of

0.2 ext{ rad/s}^2

. Calculate the torque on the plate if it rotates about a diagonal with the same angular acceleration.

Options

A $5.0 \times 10^{-6} \text{ N m}$
B $1.0 \times 10^{-5} \text{ N m}$
C $2.0 \times 10^{-5} \text{ N m}$
D $8.0 \times 10^{-6} \text{ N m}$

Correct answer

A. $5.0 \times 10^{-6} \text{ N m}$

Step-by-step solution

For a square lamina, the moment of inertia about any axis in its plane through the center is

I = \dfrac{1}{12} m a^2

. Here

m = 0.12 \text{ kg}

and

a = 0.05 \text{ m}

. Thus

I = \dfrac{1}{12}(0.12)(0.05^2) = 2.5 \times 10^{-5} \text{ kg m}^2

. The torque is

\tau = I\alpha = (2.5 \times 10^{-5})(0.2) = 5.0 \times 10^{-6} \text{ N m}

.

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