A lead ball at 30°C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely melts just before reaching the ground. The molten substance falls slowly on the ground. If the specific heat of lead = 126 Jkg-1oc-1 and a melting point of lead = 330°C and suppose that any mechanical energy lost is used to heat the ball, then the latent heat of fusion of lead is:
1. 2.4 × 104 J kg-1
2. 3.6 × 104 J kg-1
3. 7.6 × 102 J kg-1
4. 42 × 103 J kg-1
1. 2.4 × 104 J kg-1
2. 3.6 × 104 J kg-1
3. 7.6 × 102 J kg-1
4. 42 × 103 J kg-1
1. 4.5 x 106 A
2. 3.2 x 10-5 A
3. 9.8 x 10-6 A
4. 6.7 x 10-4 A
1. 27 MV
2. 18 MV
3. 20 MV
4. 23 MV
The resistance of a pair of rods is:
(
and 
\((\rho_{_{al}}=2.6\times10^{-6})~\Omega-m\) and \((\rho_{_{Cu}}=1.7\times10^{-8})~\Omega-m\)1. 1.0 m\(\Omega\)
2. 2.0 m\(\Omega\)
3. 3.0 m\(\Omega\)
4. None of these
A particle is subjected to two simple harmonic motions along the X-axis while the other is along a line making an angle of 45° with the X-axis. The two motions are given by \(x = x_0\) sin \(\omega t\) and \(s = s_0\) sin \(\omega t\). The amplitude of the resultant motion is:
1. \(x_0+s_0+2x_0s_0\)
2. \(\sqrt{x^2_0+s^2_0}\)
3. \(\sqrt{x^2_0+s^2_0+2x_0s_0}\)
4. \(x^2_0=s^2_0+\sqrt2x_0s_0~^{1/2}\)
What is the change in the volume of \(1.0~\mathrm{L}\) kerosene when it is subjected to an extra pressure of \(2.0 \times 10^5 \mathrm{~Nm}^{-2}\) from the following data?
(The density of kerosene \(=800~\mathrm{kgm^3}\) and the speed of sound in kerosene \(=1330~\mathrm{ms^{-1}}\))
1. \(
0.97 \mathrm{~cm}^{-3}
\)
2. \( 0.66 \mathrm{~cm}^{-3} \)
3. \(
0.15 \mathrm{~cm}^{-3}
\)
4. \(0.59 \mathrm{~cm}^{-3}\)
(Take \(g=10\) ms-2.)
1. \( 30 \mathrm{~m} / \mathrm{s} \)
2. \(42 \mathrm{~m} / \mathrm{s} \)
3. \( 46 \mathrm{~m} / \mathrm{s} \)
4. \( 50 \mathrm{~m} / \mathrm{s} \)
1. 5.9
2. 4.9
3. 2.9
4. 1 .9
1. \(4.3 \times 10^4 \mathrm{~N} / \mathrm{m}^2 \)
2. \( 1.8 \times 10^7 \mathrm{~N} / \mathrm{m}^2 \)
3. \( 2.1 \times 10^5 \mathrm{~N} / \mathrm{m}^2 \)
4. \(3.7 \times 10^4 \mathrm{~N} / \mathrm{m}^2\)
Water level is maintained in a cylindrical vessel up to a fixed height \(H.\) The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?
1. \(h=\frac{H}{2}\)
2. \(h=\frac{3H}{2}\)
3. \(h=\frac{2H}{3}\)
4. \(h=\frac{3}{4}H\)
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