Correct Answer: D. 1.36kgm^-3

Explanation

M_p = 1 x 40 = 40kg ; mQ = 1.6 x 60 = 96kg

volume of mixture = 40 + 60 = 100m³

mass of mixture = 40 + 96 = 136kg

density of mixture = \(\frac{136}{100}\)

= 1.36kgm³

Correct Answer: A. electrical energy to mechanical energy

Correct Answer: B. 27k

Explanation

30°C + 273 = 303K

57°C + 273 = 330K

?T = 330K - 303K

→ 27K

Explanation

a. Strain energy is the potential energy stored within an elastic material as a result of its deformation caused by external forces.

b. Energy stored E = \(\frac{1}{2}Fe\)

Young Modulus = \(\frac{ Stress}{ Strain}\) = Y

Stress = \(\frac{Force}{Area} = \frac{(F)}{(A)}\)

Strain = \(\frac{ Extension}{Original Length} = \frac{(e)}{(l)}\)

Y = \(\frac{F}{A}\div \frac{e}{l}\)

Y = \(\frac{F}{A} \times \frac{l}{e}\)

F = \(\frac{YAe}{l}\)

Therefore, Energy stored E = \(\frac{1}{2}\frac{YAe}{l}\times e\)

E = \(\frac{YAe^2}{2l}\)

Correct Answer: A. controls the flow of current

Correct Answer: C. with which the earth attracts one kilo-gram mass

Correct Answer: C. Gold-leaf electroscope

Correct Answer: C. I and II only

Explanation

ai. The heater, often referred to as the filament, is responsible for emitting electrons when heated.

ii. The high tension source, or high voltage generator, provides the high voltage necessary to accelerate the electrons emitted from the filament towards the anode (target) of the X-ray tube.

iii. Cooling fins are designed to dissipate the heat generated during the operation of the X-ray tube.

bi. The X-ray tube is highly evacuated so that the accelerated electrons can get to their target without losing much of their energy.

ii. The target is a metal with a very high melting point to withstand the high temperature generated when the electrons strike the target.

iii. The cooling fins are placed outside the glass envelope to ensure that the heat generated within the X-ray tube is efficiently transferred to the external environment.

ci. \(^{235}U_{92} + ^1_0n → ^{93}Kr_{36} + ^{141}Ba_{56} + 2^1_0n + Q\)

ii. Energy, Q, is released because the total mass on the left-hand side (reactant) is more than the total mass on the right-hand side (product). So, the energy is released in the form of a reduction in total mass. This missing mass is known as the 'mass defect' and it accounts for the energy released. Also, it's induced fission and nuclear fission is a process in which an unstable nucleus splits into two other lighter nuclei together with several neutrons and is accompanied by the release of energy.

iii. E = ?\(mc^2\) where ?m is the mass defect.

Total mass on the LHS:

235.044 u + 1.009 u = 236.053 u

Total mass on the RHS:

91.898 u + 140.914 u + 2(1.009 u) = 234.83 u

Mass defect, ?m = 236.053 u - 234.83 u = 1.223 u

?m = 1.223 × 1.66 × \(10^{-27}\) = 2.03 × \(10^{-27}\) kg

So,

E = 2.03 × \(10^{-27}\) × (3 × \(10^8)^2\)

= 1.827 × \(10^{-10}\) J

Correct Answer: C. 15.5 ms^-1

Explanation

Av. speed = \(\frac{3 \times 15 + 3 \times 10 + 4 \times 20}{3 + 3 + 4}\)

= 15.5 ms\(^{-1}\)