Q. No.A bob of mass \(m\) attached to an inextensible string of length \(l\) is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \(\omega\) rad/s about the vertical. About the point of suspension:
| 1. | angular momentum changes in magnitude but not in direction. |
| 2. | angular momentum changes in direction but not in magnitude. |
| 3. | angular momentum changes in both direction and magnitude. |
| 4. | angular momentum is conserved. |
A mass ‘\(m\)’ is supported by a massless string wound around a uniform hollow cylinder of mass \(m\) and radius \(R\). If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
1. \(\frac{g}{2}\)
2. \(\frac{5g}{6}\)
3. \(g\)
4. \(\frac{2g}{3}\)
Distance of the centre of mass of a solid uniform cone from its vertex is \(Z_0\). If the radius of its base is \(R\) and its height is \(h\) then \(Z_0\) is equal to:
1. \( \frac{{h}^2}{4{R}} \)
2. \(\frac{3 h}{4} \)
3. \(\frac{5 h}{8} \)
4. \(\frac{3{h}^2}{8{R}}\)
From a solid sphere of mass \(M\) and radius \(R\) a cube of maximum possible volume is cut. The moment of inertia of a cube about an axis passing through its center and perpendicular to one of its faces is:
1. \( \frac{{MR}^2}{32 \sqrt{2 \pi}} \)
2. \( \frac{{MR}^2}{16 \sqrt{2} \pi} \)
3. \( \frac{4 {MR}^2}{9 \sqrt{3} \pi} \)
4. \( \frac{4{MR}^2}{3 \sqrt{3} \pi}\)
1. \({I}>\dfrac{{ma}^2}{12}\)
2. \({I}=\dfrac{{ma}^2}{12}\)
3. \(\dfrac{{ma}^2}{24}<{I}<\dfrac{{ma}^2}{12}\)
4. \({I}=\dfrac{{ma}^2}{24}\)
1. \({ma}\)
2. \(2{ma}\)
3. \(\frac{5}{3}{ma}\)
4. \(\frac{3}{2}{ma}\)
1. \(14.4~\text{kg m}^2\text{s}^{-1}\)
2. \(8.64~\text{kg m}^2\text{s}^{-1}\)
3. \(20.16~\text{kg m}^2\text{s}^{-1}\)
4. \(11.52~\text{kg m}^2\text{s}^{-1}\)
1. \({a=2b}\)
2. \({2a=b}\)
3. \({a=b}\)
4. \({3a=2b}\)
A particle of mass \(m\) is moving along side of a square of side '\(a\)', with a uniform speed \(v\) in the x-y plane as shown in the figure:
Which of the following statements is false for the angular momentum \(\vec L\) about the origin?
| 1. | \(\vec{L}=-\frac{m vR}{\sqrt{2}} \hat{k}\) when the particle is moving from \(A\) to \(B\). |
| 2. | \(\vec{L}=m v\left[\frac{R}{\sqrt{2}}+a\right] \hat{k} \) when the particle is moving from \(C\) to \(D\). |
| 3. | \(\vec{L}=m v\left[\frac{R}{\sqrt{2}}+a\right] \hat{k}\) when the particle is moving from \(B\) to \(C\). |
| 4. | \(\vec{L}=\frac{m vR}{\sqrt{2}} \hat{k}\) when the particle is moving from \(D\) to \(A\). |
| 1. | The left arm is shorter than the right arm |
| 2. | Both the arms are the same length |
| 3. | Every object that is weighted using this balance appears lighter than its actual weight. |
| 4. | The left arm is longer than the right arm |
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