Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk upon the moving escalator will be:
1. \(\frac{t_1t_2}{t_2-t_1}\)
2. \(\frac{t_1t_2}{t_2+t_1}\)
3. \(t_1-t_2\)
4. \(\frac{t_1+t_2}{2}\)
A beam of light from a source \(L\) is incident normally on a plane mirror fixed at a certain distance \(x\) from the source. The beam is reflected back as a spot on a scale placed just above the source \(L\). When the mirror is rotated through a small angle \(\theta,\) the spot of the light is found to move through a distance \(y\) on the scale. The angle \(\theta\) is given by:
1. \(\frac{y}{x}\)
2. \(\frac{x}{2y}\)
3. \(\frac{x}{y}\)
4. \(\frac{y}{2x}\)
If \(\phi_1\) and \(\phi_2\) are the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip \(\phi\) is given by:
1. \(cos^2{\phi}=cos^2{\phi_1}+cos^2{\phi_2}\)
2. \(sec^2{\phi}=sec^2{\phi_1}+sec^2{\phi_2}\)
3. \(tan^2{\phi}=tan^2{\phi_1}+tan^2{\phi_2}\)
4. \(cot^2{\phi}=cot^2{\phi_1}+cot^2{\phi_2}\)
Two cars moving in opposite directions approach each other at speeds of 22 m/s and 16.5 m/s, respectively. The driver of the first car blows a horn with a frequency of 400 Hz. The frequency heard by the driver of the second car is [assume velocity of sound to be 340 m/s]:
1. 361 Hz
2. 411 Hz
3. 448 Hz
4. 350 Hz
A massless and inextensible string connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) of masses \(3m\) and \(m,\) respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of \(\mathrm{A}\) and \(\mathrm{B}\) immediately after the string is cut, are respectively:
1. | \(\frac{g}{3},g\) | 2. | \(g,g\) |
3. | \(\frac{g}{3},\frac{g}{3}\) | 4. | \(g,\frac{g}{3}\) |
A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)
The acceleration due to gravity at a height \(1~\text{km}\) above the earth's surface is the same as at a depth \(d\) below the surface of the earth. Then:
1. | \(d= 1~\text{km}\) | 2. | \(d= \frac{3}{2}~\text{km}\) |
3. | \(d= 2~\text{km}\) | 4. | \(d= \frac{1}{2}~\text{km}\) |
A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F. because the method involves:
1. | the potential gradients. |
2. | a condition of no current flow through the galvanometer. |
3. | a condition of cells, galvanometer, and resistances. |
4. | the cells. |
A spherical black body with a radius of \(12\) cm radiates \(450\) W power at \(500\) K. If the radius were halved and the temperature is doubled, the power radiated in watts would be:
1. \(450\)
2. \(1000\)
3. \(1800\)
4. \(225\)