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Heat energy = Electrical energy mc\(\theta\) = power x time 5 x 1 x 10-2 x C = 100 x 20 C = 4.0 x 104Jkg-1k-1

\(\frac{P_2V_2}{T_2}\) = \(\frac{P_1V_1}{T_1}\) P2 = 2P1 T1 = 2T2 \(\frac{2P_1V_2}{T_2}\) = \(\frac{P_1V_1}{2T_1}\) Change in volume = \(V_2 - V_1\) % change = \(\frac{V_1 - \frac{1}{4}V_1}{V_1}\) X 100% = 75%

Increasing the rotation speed enhances the electromotive force (EMF) generated due to Faraday's law of electromagnetic induction.

Gun momentum = bullet momentum 2 x v = 1.6 x 10-2 x 150 v = 1.2ms-1 in opposite direction

power = \(\frac{\text{work done}}{time}\) = \(\frac{1000 \times 10 \times 10}{10}\) = 10kW

v = F\(\lambda\) 3 x 108 = \(\lambda\) x 800 x 103 \(\lambda\) = 375.0m

PT = (5 x 50) + (100 x 4) = 650watts Energy(kWhr) = 650 x 10-3 x 10 = 6.5 kWhr 1kWhr cost 2 kobo ; 6.5 kWhr will cost \(\frac{2 \times 6.5}{1}\) = 13 kobo

The graph shows the force decreasing linearly from 20 N at 0 m to 0 N at 20 m. For the first 10 m: - Force at 0 m = 20 N - Force at 10 m = 10 N (midway) The area under the graph (work done) is the area of a trapezium: \(\text{Work} = \frac{1}{2} \times (20 + 10) \times 10 = 15 \times 10 = \mathbf{150\, J}\).

P = \(\frac{ V^2}{R}\) \(P_1 R_1 = P_2 R_2\) ( Parallel circuit) 10 x 4 = \(P_2\) x 6 \(P_2\) = \(\frac{40}{6}\) = 6.7W.

\(\lambda_1\) = 4L\(_1\) and \(\lambda_2\) = \(\frac{4L_1}{3}\) f\(\lambda\) = velocity But f = \(\frac{V}{\lambda}\) F\(_1\) = \(\frac{V}{4L_1}\) and F\(_2\) = \(\frac{3V}{4L_1}\) \(\frac{F_2}{F_1}\) = \(\frac{\frac{3V}{4L_1}}{\frac{V}{4L_1}}\) = 3 Note: The next frequency F\(_2\) that gives resonance will correspond to the third harmonic, which supports three-quarters of a wavelength

- Static Friction is friction which is experienced when an object is placed on a surface. And, Kinetic friction is due to the movement of an object on a surface. - Static friction is greater than kinetic friction because there are more forces at work keeping an object stationary than there are forces working to resist an object once it is in motion. - Rolling friction is the weakest type of friction, static being the strongest. The frictional force depends on the area of contact between the two bodies. As the area of contact is less in rolling friction than the sliding friction, so rolling friction is weaker than sliding friction.

No expanded working has been attached for this question yet. The verified answer is Option C.

n = \(\frac{\text{velocity of light in vacuum}}{\text{velocity of light in liquid}}\) 1.5 = \(\frac{3\times10^4}{\text{velocity of light in liquid}}\) Velocity of light in liquid = 2 x \(10^8ms^{-1}\)

R.d = 19, therefore, density = 19gcm-3 mass = volume x density = 20 x 19 = 380g

The pressure in a liquid does not depend on the shape or size of the container. The pressure in a liquid acts in all directions. The pressure exerted increases with the depth of liquid. Pressure at all points at equal depth is equal.