A balloon with mass \(m\) is descending down with an acceleration \(a\) (where \(a<g\)). How much mass should be removed from it so that it starts moving up with an acceleration \(a\)?
| 1. | \( \frac{2 m a}{g+a} \) | 2. | \( \frac{2 m a}{g-a} \) |
| 3. | \( \frac{m a}{g+a} \) | 4. | \( \frac{m a}{g-a}\) |
A body of mass (\(4m\)) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (\(m\)) move perpendicular to each other with equal speeds (\(u\)). The total kinetic energy generated due to explosion is:
| 1. | \(mu^2\) | 2. | \(1.5~mu^2\) |
| 3. | \(2~mu^2\) | 4. | \(3~mu^2\) |
The oscillation of a body on a smooth horizontal surface is represented by the equation, \(X=A \text{cos}(\omega t)\),
where \(X=\) displacement at time \(t,\) \(\omega=\) frequency of oscillation.
Which one of the following graphs correctly shows the variation of acceleration, \(a\) with time, \(t?\)
(\(T=\) time period)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A solid cylinder of mass \(50~\text{kg}\) and radius \(0.5~\text{m}\) is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely. The tension in the string required to produce an angular acceleration of \(2~\text{rev/s}^2\) will be:
1. \(25~\text N\)
2. \(50~\text N\)
3. \(78.5~\text N\)
4. \(157~\text N\)
The ratio of the acceleration for a solid sphere (mass \(m\) and radius \(R\)) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is:
1. \(5:7\)
2. \(2:3\)
3. \(2:5\)
4. \(7:5\)
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass\(m=5.98\times 10^{24}~\text{kg})\) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100~\text{m}\)
Dependence of intensity of gravitational field \((\mathrm{E})\) of the earth with distance \((\mathrm{r})\) from the centre of the earth is correctly represented by: (where \(\mathrm{R}\) is the radius of the earth)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
1. \(\Delta l ~\text{vs}~\dfrac{1}{l}\)
2. \(\Delta l ~\text{vs}~l^2\)
3. \(\Delta l ~\text{vs}~\dfrac{1}{l^2}\)
4. \(\Delta l ~\text{vs}~l\)
A certain number of spherical drops of a liquid of radius \({r}\) coalesce to form a single drop of radius \({R}\) and volume \({V}.\) If \({T}\) is the surface tension of the liquid, then:
| 1. | the energy \(= 4{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)\) is released. |
| 2. | the energy \(={ 3{VT}\left( \frac{1}{{r}} + \frac{1}{{R}}\right)}\) is released. |
| 3. | the energy \(={ 3{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)}\) is released. |
| 4. | the energy is neither released nor absorbed. |
[Take specific heat of water \(= 1~\text{cal g}^{-1}~^\circ\text{C}^{-1}\) and latent heat of steam \(= 540~\text{cal g}^{-1}\)]
| 1. | \(24~\text{g}\) | 2. | \(31.5~\text{g}\) |
| 3. | \(42.5~\text{g}\) | 4. | \(22.5~\text{g}\) |
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