Q. No.If a body moving in a circular path maintains a constant speed of \(10\text{ m/s},\) then which of the following correctly describes the relation between acceleration and radius?
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Subtopic: Uniform Circular Motion |
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A conical pendulum of length \(1~\text{m}\) makes an angle \(\theta=45^\circ\) with respect to the \(z\text-\)axis and moves in a circle in the \(xy\) plane. The radius of the circle is \(0.4~\text{m}\) and its center is vertically below \(O.\) The speed of the pendulum, in its circular path, will be:
(Take \({g}=10~\text{ms}^{-2})\)
1. \(0.4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(4~\text{m/s}\)
(Take \({g}=10~\text{ms}^{-2})\)
1. \(0.4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(4~\text{m/s}\)
Subtopic: Uniform Circular Motion |
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A particle is moving with a uniform speed in a circular orbit of radius \(R\) in a central force inversely proportional to the \(n^{\text{th}}\) power of \(R\). If the period of rotation of the particle is \(T\), then:
1. \(T \propto R^{3 / 2} ~\text{for any } n\)
2. \(T \propto R^{\frac{{n}}{2}+1} \)
3. \({T} \propto {R}^{({n}+1) / 2} \)
4. \( T \propto R^{n / 2} \)
Subtopic: Uniform Circular Motion |
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A uniform rod of length \(l\) is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is \(T(x)\) at a distance \(x\) from the axis, then which of the following graphs depicts it most closely?
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Subtopic: Uniform Circular Motion |
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A bead of mass \(m\) stays at point \({P (a,b)}\) on a wire bent in the shape of a parabola \(y=4Cx^2 \) and rotating with angular speed \(\omega \) (see figure). The value of \(\omega\) is (neglect friction) :
| 1. | \( \sqrt{\dfrac{2 g C}{a b}} \) | 2. | \( 2 \sqrt{2 g C}\) |
| 3. | \( \sqrt{\dfrac{2 g}{C}} \) | 4. | \( 2 \sqrt{g C} \) |
Subtopic: Uniform Circular Motion |
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A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is \({K \over \pi}~rev./min\). The value of K is: (Assume the string is massless and unstretchable)
1. 400
2. 300
3. 600
4. 800
1. 400
2. 300
3. 600
4. 800
Subtopic: Uniform Circular Motion |
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A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is:
1. the same throughout the motion.
2. minimum at the highest position of the circular path.
3. minimum at the lowest position of the circular path.
4. minimum when the rope is in the horizontal position.
1. the same throughout the motion.
2. minimum at the highest position of the circular path.
3. minimum at the lowest position of the circular path.
4. minimum when the rope is in the horizontal position.
Subtopic: Uniform Circular Motion |
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A disc with a flat small bottom beaker placed on it at a distance \(R\) from its centre is revolving about an axis passing through the centre and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if:
1. \({R} \leq \frac{\mu{g}}{2 \omega^2} \)
2. \(R \leq \frac{\mu g}{\omega^2} \)
3. \(R \geq \frac{\mu g}{2 \omega^2} \)
4. \(R \geq \frac{\mu g}{\omega^2}\)
1. \({R} \leq \frac{\mu{g}}{2 \omega^2} \)
2. \(R \leq \frac{\mu g}{\omega^2} \)
3. \(R \geq \frac{\mu g}{2 \omega^2} \)
4. \(R \geq \frac{\mu g}{\omega^2}\)
Subtopic: Uniform Circular Motion |
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A ball is released from rest from point \(P\) of a smooth semi-spherical vessel as shown in the figure. The ratio of the centripetal force and the normal reaction on the ball at point \(Q\) is \(A\) while the angular position of point \(Q\) is \(\alpha\) with respect to point \(P\). Which of the following graphs represents the correct relation between \(A\) and \(\alpha\) when the ball goes from point \(Q\) to point \(R?\)
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Subtopic: Uniform Circular Motion |
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One end of a massless spring of spring constant k and natural length \(l_0\) is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through a fixed end, then the elongation of the spring will be:
1. \(\frac{\mathrm{k}-\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2} \)
2. \( \frac{\mathrm{m} \omega^2 l_0}{\mathrm{k}+\mathrm{m} \omega^2} \)
3. \( \frac{m \omega^2 l_0}{k-m \omega^2} \)
4. \(\frac{\mathrm{k}+\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2}\)
1. \(\frac{\mathrm{k}-\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2} \)
2. \( \frac{\mathrm{m} \omega^2 l_0}{\mathrm{k}+\mathrm{m} \omega^2} \)
3. \( \frac{m \omega^2 l_0}{k-m \omega^2} \)
4. \(\frac{\mathrm{k}+\mathrm{m} \omega^2 l_0}{\mathrm{~m} \omega^2}\)
Subtopic: Uniform Circular Motion |
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