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Nuclear Physics
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Question:

Number of fission per second in a 100-MW reactor is:

Each fission of uranium nucleus releases about 200 MeV = $$320\times 10^{−13} J$$ So the number of fissions per second in a 100-MW reactor is N = $$\frac{100 \times10^6}{320\times 10^{-13}} = 10^{18}$$ Hence the answer is $$10^{18}$$.

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Question:

A spaceship travels toward the Earth at a speed of 0.97c. The occupants of the ship are standing with their torsos parallel to the direction of travel. According to Earth observers, they are about 0.50 m tall and 0.50 m wide. What are the occupants’ height and width according to others on the spaceship?

length contraction happens along the direction of motion. we know that $$L=L_0 \sqrt{1-v^2/c^2}$$ given that $$L$$ = 0.50 m, v=0.97c, $$L_0$$= ? $$L_0=\frac{L}{\sqrt{1-v^2/c^2}}$$= $$\frac{0.50}{\sqrt{1-(0.97c)^2/c^2}}$$ $$L_0=\frac{0.50}{0.243}= 2.1 m$$ hence height=2.1 m and widt =0.5m

Physics
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Question:

Find the kinetic energy of a particle of mass 0.1 kg moving with a velocity of 10 m/s?

Kinetic energy is given by the formula $$E=\frac{1}{2}mv^2$$ m= 0.1 kg, v=10 m/s Hence $$E=(0.5)(0.1)(10)^2$$ = 5 joules

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