ROTATIONAL INERTIA OF SOLID BODIES, ROTATIONAL DYNAMICS
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Rotational Motion

269320 Four point size dense bodies of same mass are attached at four corners of a light square frame. Identify the decreasing order of their moments of inertia about following axes.
I) Passing through any side
II) Passing through opposite corners
III) \(\perp^{\mathrm{r}}\) bisector of any side
IV) \(\perp^{r}\) to the plane and passing through any corner

1 III, IV, I, II
2 IV, III, I, II
3 III, II, IV, I
4 IV, III, II, I
Rotational Motion

269321 A motor car is moving in a circular path with uniform speed v. Suddenly the car rotates through an angle\(\theta\). Then, the magnitude of change in its velocity is

1 \(2 \mathrm{v} \cos \frac{\theta}{2}\)
2 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
3 \(2 v \tan \frac{\theta}{2}\)
4 \(2 \mathrm{vsec} \frac{\theta}{2}\)
Rotational Motion

269322 An electric motor rotates a wheel at a constant angular velocity\((\omega)\) while opposing torque is \(\tau\). The power of that electric motor is

1 \(\frac{\tau \omega}{2}\)
2 \(\tau \omega\)
3 \(2 \tau \omega\)
4 \(\frac{\tau}{\omega}\)
Rotational Motion

269323 A constant poweris supplied to a rotating disc. The relationship between the angular velocity \((\omega)\) of the disc and number of rotations (n) made by the disc is governed by

1 \(\boldsymbol{\omega} \propto n^{\frac{1}{3}}\)
2 \(\omega \propto n^{\frac{2}{3}}\)
3 \(\omega \propto n^{\frac{3}{2}}\)
4 \(\omega \propto n^{2}\)
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Rotational Motion

269320 Four point size dense bodies of same mass are attached at four corners of a light square frame. Identify the decreasing order of their moments of inertia about following axes.
I) Passing through any side
II) Passing through opposite corners
III) \(\perp^{\mathrm{r}}\) bisector of any side
IV) \(\perp^{r}\) to the plane and passing through any corner

1 III, IV, I, II
2 IV, III, I, II
3 III, II, IV, I
4 IV, III, II, I
Rotational Motion

269321 A motor car is moving in a circular path with uniform speed v. Suddenly the car rotates through an angle\(\theta\). Then, the magnitude of change in its velocity is

1 \(2 \mathrm{v} \cos \frac{\theta}{2}\)
2 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
3 \(2 v \tan \frac{\theta}{2}\)
4 \(2 \mathrm{vsec} \frac{\theta}{2}\)
Rotational Motion

269322 An electric motor rotates a wheel at a constant angular velocity\((\omega)\) while opposing torque is \(\tau\). The power of that electric motor is

1 \(\frac{\tau \omega}{2}\)
2 \(\tau \omega\)
3 \(2 \tau \omega\)
4 \(\frac{\tau}{\omega}\)
Rotational Motion

269323 A constant poweris supplied to a rotating disc. The relationship between the angular velocity \((\omega)\) of the disc and number of rotations (n) made by the disc is governed by

1 \(\boldsymbol{\omega} \propto n^{\frac{1}{3}}\)
2 \(\omega \propto n^{\frac{2}{3}}\)
3 \(\omega \propto n^{\frac{3}{2}}\)
4 \(\omega \propto n^{2}\)
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Rotational Motion

269320 Four point size dense bodies of same mass are attached at four corners of a light square frame. Identify the decreasing order of their moments of inertia about following axes.
I) Passing through any side
II) Passing through opposite corners
III) \(\perp^{\mathrm{r}}\) bisector of any side
IV) \(\perp^{r}\) to the plane and passing through any corner

1 III, IV, I, II
2 IV, III, I, II
3 III, II, IV, I
4 IV, III, II, I
Rotational Motion

269321 A motor car is moving in a circular path with uniform speed v. Suddenly the car rotates through an angle\(\theta\). Then, the magnitude of change in its velocity is

1 \(2 \mathrm{v} \cos \frac{\theta}{2}\)
2 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
3 \(2 v \tan \frac{\theta}{2}\)
4 \(2 \mathrm{vsec} \frac{\theta}{2}\)
Rotational Motion

269322 An electric motor rotates a wheel at a constant angular velocity\((\omega)\) while opposing torque is \(\tau\). The power of that electric motor is

1 \(\frac{\tau \omega}{2}\)
2 \(\tau \omega\)
3 \(2 \tau \omega\)
4 \(\frac{\tau}{\omega}\)
Rotational Motion

269323 A constant poweris supplied to a rotating disc. The relationship between the angular velocity \((\omega)\) of the disc and number of rotations (n) made by the disc is governed by

1 \(\boldsymbol{\omega} \propto n^{\frac{1}{3}}\)
2 \(\omega \propto n^{\frac{2}{3}}\)
3 \(\omega \propto n^{\frac{3}{2}}\)
4 \(\omega \propto n^{2}\)
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Rotational Motion

269320 Four point size dense bodies of same mass are attached at four corners of a light square frame. Identify the decreasing order of their moments of inertia about following axes.
I) Passing through any side
II) Passing through opposite corners
III) \(\perp^{\mathrm{r}}\) bisector of any side
IV) \(\perp^{r}\) to the plane and passing through any corner

1 III, IV, I, II
2 IV, III, I, II
3 III, II, IV, I
4 IV, III, II, I
Rotational Motion

269321 A motor car is moving in a circular path with uniform speed v. Suddenly the car rotates through an angle\(\theta\). Then, the magnitude of change in its velocity is

1 \(2 \mathrm{v} \cos \frac{\theta}{2}\)
2 \(2 \mathrm{v} \sin \frac{\theta}{2}\)
3 \(2 v \tan \frac{\theta}{2}\)
4 \(2 \mathrm{vsec} \frac{\theta}{2}\)
Rotational Motion

269322 An electric motor rotates a wheel at a constant angular velocity\((\omega)\) while opposing torque is \(\tau\). The power of that electric motor is

1 \(\frac{\tau \omega}{2}\)
2 \(\tau \omega\)
3 \(2 \tau \omega\)
4 \(\frac{\tau}{\omega}\)
Rotational Motion

269323 A constant poweris supplied to a rotating disc. The relationship between the angular velocity \((\omega)\) of the disc and number of rotations (n) made by the disc is governed by

1 \(\boldsymbol{\omega} \propto n^{\frac{1}{3}}\)
2 \(\omega \propto n^{\frac{2}{3}}\)
3 \(\omega \propto n^{\frac{3}{2}}\)
4 \(\omega \propto n^{2}\)