A metal rod at a temperature of \(145^\circ\mathrm{C}\), radiates energy at a rate of \(17~\mathrm{W}\). If its temperature is increased to \(273^\circ\mathrm{C}\), then it will radiate at the rate of:
1. \( 49.6 \mathrm{~W} \)
2. \( 17.5 \mathrm{~W} \)
3. \( 50.3 \mathrm{~W} \)
4. \(67.5 \mathrm{~W}\)
 

A square wire of side \(2.0~\mathrm{cm}\) is placed \(20~\mathrm{cm}\) in front of a concave mirror of focal length \(10~\mathrm{cm}\) with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of wire is:
1. \( 7.5 \mathrm{~cm}^2 \)
2. \( 6 \mathrm{~cm}^2 \)
3. \(2 \mathrm{~cm}^2 \)
4. \( 4 \mathrm{~cm}^2\)
 

A lead bullet penetrates into a solid and melts. Assuming that \(50\%\) of its kinetic energy was used to heat it, the initial speed of the bullet is: (the initial temperature of the bullet is \(25^\circ\mathrm{C} \) and its melting point is \(300^\circ\mathrm{C} \)). Latent heat of fusion of lead \(=2.5\times10^4~\mathrm{J/Kg}\) and specific heat capacity of lead \(=125~\mathrm{J/Kg-K}\).
1. \( 100 \mathrm{~m} / \mathrm{s} \)
2. \( 490 \mathrm{~m} / \mathrm{s} \)
3. \( 520 \mathrm{~m} / \mathrm{s} \)
4. \( 360 \mathrm{~m} / \mathrm{s}\)
 

The concentric, conducting spherical shells \(X,~ Y\) and \(Z\) with radii \(r, ~2r\) and \(3r\) respectively. \(X\) and \(Z\) are connected by a conducting wire and \(Y\) is uniformly charged to charge \(Q\) as shown in the figure. Charges on shells \(X\) and \(Z\) will be:

1. \(qx=\frac{Q}{4},qz=\frac{-Q}{6}\)
2. \(qx=\frac{-Q}{4},qz=\frac{Q}{4}\)
3. \(qx=\frac{Q}{4},qz=\frac{-Q}{4}\)
4. \(qx=\frac{-Q}{6},qz=\frac{Q}{4}\)

The temperature of a gas is raised from \(27^\circ\mathrm{C}\) to \(927^\circ\mathrm{C}\). The root mean square speed:

A particle slides down on a smooth incline of inclination ${\mathrm{30°}}^{}$, fixed in an elevator going up with an acceleration of 2 m/s². The box of incline has a length of 4 m. The time taken by the particle to reach the bottom will be: 

1. \(\frac89\sqrt3s\)
2. \(\frac98\sqrt3s\)
3. \(\frac43\sqrt{\frac{\sqrt3}{2}}s\)
4. \(\frac34\sqrt{\frac{\sqrt3}{2}}s\)

A stone projected with a velocity \(u\) at an angle \(\Big(\frac{\pi}{2}-\theta\Big)\) with the horizontal reaches maximum height \(H_1\) When it is projected with velocity \(u\) at an angle with the horizontal, it reaches maximum height Hz. The relation between the horizontal range \(R\) of the projectile, \(H_1\) and \(H_2\) is:
1. \(R=4\sqrt{H_1H_2}\)
2. \(R=4({H_1-H_2})\)
3. \(R=4({H_1+H_2})\)
4. \(R=\frac{H^2_1}{H_2^2}\)