A biconvex lens has power \(P.\) It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be:
| 1. | \(0\) | 2. | \(\dfrac{P}{2}\) |
| 3. | \(\dfrac{P}{4}\) | 4. | \(P\) |
In Young's double-slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has a path difference:
| 1. | \( \dfrac{5\lambda}{2} \) | 2. | \( \dfrac{10\lambda}{2} \) |
| 3. | \( \dfrac{9\lambda}{2} \) | 4. | \( \dfrac{11\lambda}{2} \) |
A double convex lens has a focal length of \(25\) cm. The radius of curvature of one of the surfaces is double of the other. What would be the radii if the refractive index of the material of the lens is \(1.5?\)
1. \(100\) cm, \(50\) cm
2. \(25\) cm, \(50\) cm
3. \(18.75\) cm, \(37.5\) cm
4. \(50\) cm, \(100\) cm
Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being \(100~\text{m}\) apart and being of the same height of \(200~\text{m}\)) with the same velocity of \(25~\text{m/s}.\) When and where will the two bullets collide?
\((g = 10~\text{m/s}^2)\)
| 1. | After \(2~\text{s}\) at a height of \(180~\text{m}\) |
| 2. | After \(2~\text{s}\) at a height of \(20~\text{m}\) |
| 3. | After \(4~\text{s}\) at a height of \(120~\text{m}\) |
| 4. | They will not collide. |
The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):
| 1. | ductile and brittle |
| 2. | brittle and ductile |
| 3. | brittle and plastic |
| 4. | plastic and ductile |
A body of mass \(m\) is kept on a rough horizontal surface (coefficient of friction = \(\mu).\) A horizontal force is applied to the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by \(\vec {F}\) where:
1. \(|{\vec {F}}| = mg+\mu mg\)
2. \(|\vec {F}| =\mu mg\)
3. \(|\vec {F}| \le mg\sqrt{1+\mu^2}\)
4. \(|\vec{F}| = mg\)
A particle of mass \(5m\) at rest suddenly breaks on its own into three fragments. Two fragments of mass \(m\) each move along mutually perpendicular directions with speed \(v\) each. The energy released during the process is:
| 1. | \(\dfrac{3}{5}mv^2\) | 2. | \(\dfrac{5}{3}mv^2\) |
| 3. | \(\dfrac{3}{2}mv^2\) | 4. | \(\dfrac{4}{3}mv^2\) |
An object of mass \(500~\text g\) initially at rest is acted upon by a variable force whose \(x\)-component varies with \(x\) in the manner shown. The velocities of the object at the points \(x=8~\text m\) and \(x=12~\text m\) would have the respective values of nearly:
| 1. | \(18~\text {m/s}\) and \(22.4~\text {m/s}\) | 2. | \(23~\text {m/s}\) and \(22.4~\text {m/s}\) |
| 3. | \(23~\text {m/s}\) and \(20.6~\text {m/s}\) | 4. | \(18~\text {m/s}\) and \(20.6~\text {m/s}\) |
A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle of inclination . The centre of mass of the cylinder has a speed of 4 m/s. The distance travelled by the cylinder on the inclined surface will be
| 1. | 2.2 m | 2. | 1.6 m |
| 3. | 1.2 m | 4. | 2.4 m |
Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i,\) what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)
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