Answer True, False, or Cannot tell to each of the four statements below. E.g., i

Question

Answer True, False, or Cannot tell to each of the four statements below. E.g., if the answer to the first statement is `true' and to the rest, `cannot tell', enter TCCC.

a.A square plate can rotate about an axle through its centre. One of three forces of equal magnitude can be applied to the plate, as shown. The angular acceleration of the plate is the same whichever of the forces is applied.

b.The solid cylinders and the cylindrical shells have the same mass, the same radius, and turn on frictionless axles. A rope is wrapped around each of them and is acted on as shown. Cylinder shell 3 has the smallest angular acceleration.

c.A wheel turns on a frictionless axle. A string wrapped around the rim of the wheel is connected to a mass. When the mass is released, the magnitude of its acceleration is equal to g.

d.If force F2 was reversed, the object would not rotate about the axle. (Note: F1 = F2 < F3)

Explanation / Answer

a) False

By equation below

F*r= I*alpha

Angular acceration alpha depends on r i.e. distance of applivcation of force from axis or rotation.

Thus The angular acceleration of the plate is not the same whichever of the forces is applied.

b) False

By equation below

F*r= I*alpha

Angular acceration alpha depends on I i.e. moment of inertia

Ishell = mr^2

Icylinder = mr^2/2

Since   Ishell > Icylinder    => alpha(shell) < alpha(cylinder)

But since 3 and 4 are both shell and all vaues i.e. F , r and I are same for both both have same alpha i.e. angular acceleration.

c) False

By equation below

F*r= I*alpha

I= Idisk = mr^2/2

F= mg

mg*r = mr^2/2*aplha

gives , apha = 2g/r which is not equal to g.

d) True

F3 will not contribute to the torque since force is applied to parallel distance.

Now

Tnet = F1*d1 - F2*d2*sin60 = F1*d1 - 0.87*F2*d2 =0

Since F1=F2   if d1= 0.87*d2   => Tnet =0

Thus there would not be torque about the axle.

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