Q. No.A uniform rod of mass \(m\) and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is: (\(g\) acceleration due to gravity)
1. \(\dfrac{mg}{2}\)
2. \(\dfrac{mg}{4}\)
3. \(\dfrac{mg}{3}\)
4. \(mg\)
1. \(\dfrac{mg}{2}\)
2. \(\dfrac{mg}{4}\)
3. \(\dfrac{mg}{3}\)
4. \(mg\)
Subtopic: Torque |
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Two masses \(400 ~\text g\) and \(350 ~\text g\) are suspended from the ends of a light string passing over a heavy pulley of radius \(2 ~\text {cm}.\) When released from rest the heavier mass is observed to fall \(81 ~\text {cm}\) in \(9 ~\text {s}.\) The rotational inertia of the pulley is: (in \(\text {kg.}\text m^2\))
\(\left({g}=9.8 ~\text{m/s}^2 \right)\)
1. \( 9.5 \times 10^{-3}\)
2. \(4.75 \times 10^{-3}\)
3. \( 1.86 \times 10^{-2}\)
4. \(8.3 \times 10^{-3}\)
\(\left({g}=9.8 ~\text{m/s}^2 \right)\)
1. \( 9.5 \times 10^{-3}\)
2. \(4.75 \times 10^{-3}\)
3. \( 1.86 \times 10^{-2}\)
4. \(8.3 \times 10^{-3}\)
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Which of the following are correct expression for torque acting on a body?
( \(\vec{\tau}=\) position vector; \(\vec{p}=\) linear momentum; \(\vec{L}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration; \(I=\) moment of inertia; \( \vec{F}=\) force; \(t =\) time)
Choose the correct answer from the options given below:
| \(\mathrm{A.}\) | \(\vec{\tau}=\vec{r} \times \vec{L}\) |
| \(\mathrm{B.}\) | \( \vec{\tau}=\frac{d}{d t}(\vec{r} \times \vec{p})\) |
| \(\mathrm{C.}\) | \(\vec{\tau}=\vec{r} \times \frac{d \vec{p}}{d t}\) |
| \(\mathrm{D.}\) | \(\vec{\tau}=I \vec{\alpha}\) |
| \(\mathrm{E.}\) | \(\vec{\tau}=\vec{r} \times \vec{F}\) |
Choose the correct answer from the options given below:
| 1. | \(\mathrm{A,B,D~\text{and}~E~\text{Only}}\) | 2. | \(\mathrm{C~\text{and}~D~\text{Only}}\) |
| 3. | \(\mathrm{B,C,D~\text{and}~E~\text{Only}}\) | 4. | \(\mathrm{B,D~\text{and}~E~\text{Only}}\) |
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A thin solid disk of \(1~\text{kg}\) is rotating along its diameter axis at the speed of \(1800~\text{rpm.} \) By applying an external torque of \(25π~ \text{Nm for }40 ~\text s, \) the speed increases to \(2100~\text{rpm.}\)The diameter of the disk is:
1. \(10~\text{m}\)
2. \(20~\text{m}\)
3. \(30~\text{m}\)
4. \(40~\text{m}\)
1. \(10~\text{m}\)
2. \(20~\text{m}\)
3. \(30~\text{m}\)
4. \(40~\text{m}\)
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A square Lamina \(OABC \) of length \(10 ~\text{cm}\) is pivoted at \(O.\) Forces act at Lamina as shown in figure. If lamina remains stationary, then the magnitude of \(F \) is:
1. \(10~\text N \)
2. \(10\sqrt2~\text N ~\)
3. \(0~\text N \)
4. \(20~\text N \)
1. \(10~\text N \)
2. \(10\sqrt2~\text N ~\)
3. \(0~\text N \)
4. \(20~\text N \)
Subtopic: Torque |
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A uniform rod of mass \(250~\text{g}\) having length \(100~\text{cm}\) is balanced on a sharp edge at \(40~\text{cm}\) mark. A mass of \(400 ~\text{g}\) is suspended at \(10 ~\text{cm}\) mark. To maintain the balance of the rod, the mass to be suspended at \(90~\text{cm}\) mark, is
1. \(290~\text{g}\)
2. \(190~\text{g}\)
3. \(300~\text{g}\)
4. \(200~\text{g}\)
1. \(290~\text{g}\)
2. \(190~\text{g}\)
3. \(300~\text{g}\)
4. \(200~\text{g}\)
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The coordinates of a particle with respect to origin in a given reference frame is (\(1, 1, 1\)) meters. If a force of
1. \(2~\text{N.m}\)
2. \(0~\text{N.m}\)
3. \(1~\text{N.m}\)
4. \(4~\text{N.m}\)
1. \(2~\text{N.m}\)
2. \(0~\text{N.m}\)
3. \(1~\text{N.m}\)
4. \(4~\text{N.m}\)
Subtopic: Torque |
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The torque due to the force \(( 2 \hat i + \hat j + 2 \hat k) \) about the origin, acting on a particle whose position vector is \((\hat i + \hat j + \hat k) \) would be
1. \(\hat i + \hat k \)
2. \(\hat i - \hat j + \hat k \)
3. \(\hat j + \hat k \)
4. \(\hat i - \hat k \)
1. \(\hat i + \hat k \)
2. \(\hat i - \hat j + \hat k \)
3. \(\hat j + \hat k \)
4. \(\hat i - \hat k \)
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A heavy iron bar, of weight \(W\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is :
1. \(W / 2\)
2. \(W \sin \theta\)
3. \(W\)
4. \(W \cos \theta\)
1. \(W / 2\)
2. \(W \sin \theta\)
3. \(W\)
4. \(W \cos \theta\)
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A man holding a rod of mass \(m\) as shown in the figure. Find the weight of the rod experienced by him.
1. \(mg\over 2\)
2. \({mg}\over 4\)
3. \(3{mg}\over 2\)
4. \({mg}\over 3\)
1. \(mg\over 2\)
2. \({mg}\over 4\)
3. \(3{mg}\over 2\)
4. \({mg}\over 3\)
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