Explanation

• The formula for the period of a pendulum is T = 2π√(l/g), where l is the length of the pendulum and g is the acceleration due to gravity.
• Since the mass and diameter are doubled, the acceleration due to gravity (g) on the planet will be half that of Earth.
• Therefore, the new period of oscillation will be √2 times the period on Earth, meaning if it was a second's pendulum on Earth, it will be 2√2 seconds on the planet.

Explanation

Initial efficiency (η) = 40% = 0.4

Sink temperature (Tc) = 300 K

Initial source temperature (Th) = 300 / (1 - 0.4) = 500 K

New efficiency (η_new) = 0.4 + 0.5(0.4) = 0.6

New source temperature (Th_new) = 300 / (1 - 0.6) = 750 K

Increase in temperature = Th_new - Th = 750 - 500 = 250 K

Explanation

Explanation

Since μ = 1/√3, we can use the fact that μ = tan(θ) when the block just slides down the inclined plane.

μ = 1/√3 = tan(θ)

θ = arctan(1/√3)

θ = 30°

Explanation

Given:

Energy of photon (E) = 4.1 MeV

The total energy available for the electron and positron is:

E - 2 × 0.511 MeV = 4.1 MeV - 1.022 MeV = 3.078 MeV

Since the electron and positron share the energy equally, the kinetic energy of the electron is:

3.078 MeV / 2 = 1.539 MeV

Adding the rest mass energy of the electron (0.511 MeV), we get:

Energy of electron = 1.539 MeV + 0.511 MeV = 2.05 MeV

Explanation

Explanation

Explanation

Explanation

Explanation

To find the moment of inertia (I) of the rotating body, we can use the formula:

τ = I × α

where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

Given:

τ = 2 × 10^-4 Nm

α = 4 rad/s^2

Rearranging the formula to solve for I:

I = τ / α

= (2 × 10^-4 Nm) / (4 rad/s^2)

= 0.5 × 10^-4 kgm^2