Q. No.A wheel is rotating about an axis through its centre at \(720~\text{rpm}.\) It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally.
The value of torque in \((\text{N-m })\) is:
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\)
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\)
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)
1. \(\frac{5}{7}g\sin\theta\)
2. \(\frac{3}{5}g\sin\theta\)
3. \(\frac{2}{7}g\sin\theta\)
4. \(\frac{2}{5}g\sin\theta\)
A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 2r and thickness . The relation between moments of inertia and is
1.
2.
3.
4. Depends on the actual values of t and r
A particle of mass 2 kg located at the position m has a velocity of 2 m/s. Its angular momentum about z-axis in kg- is :
1. +4
2. +8
3. -4
4. -8
A solid cylinder of mass 'M' is suspended by two strings wrapped around it as shown. The acceleration 'a' and the tension T when the cylinder falls and the string unwinds itself are, respectively,
1. \(a=g,~T=\dfrac{Mg}{2}\)
2. \(a=\dfrac{g}{2},~T=\dfrac{Mg}{2}\)
3. \(a=\dfrac{g}{3},~T=\dfrac{Mg}{3}\)
4. \(a=\dfrac{2g}{3},~T=\dfrac{Mg}{6}\)
An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?
1. 350 N-m
2. 440 N-m
3. 531 N-m
4. 628 N-m
In an orbital motion, the angular momentum vector is
1. Along the radius vector
2. Parallel to the linear momentum
3. In the orbital plane
4. Perpendicular to the orbital plane
A particle of mass \(m\) moves with a constant velocity along \(3\) different paths, \(DE, OA\) and \(BC\). Which of the following statements is not correct about its angular momentum about point \(O\)?
| 1. | It is zero when it is at \(A\) and moving along \(OA\). |
| 2. | The same at all points along the line \(DE\). |
| 3. | Of the same magnitude but oppositely directed at \(B\) and \(D\). |
| 4. | Increases as it moves along the line \(BC\). |
In free space, a rifle of mass \(M\) shoots a bullet of mass \(m\) at a stationary block of mass \(M\) at a distance \(D\) away from it. When the bullet has moved through a distance \(d\) towards the block, the centre of mass of the bullet-block system is at a distance of:
1. \(\frac{D-d}{M+m}~\text{from the bullet}\)
2. \(\frac{md+ MD}{M+m}~\text{from the block}\)
3. \(\frac{2md+ MD}{M+m}~\text{from the block}\)
4. \(\frac{(D-d)M}{M+m}~\text{from the bullet}\)
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