Explanation

Explanation

To calculate the velocity attained by the rocket, we can use the equation:

F × t = m × Δv

where:

F = force applied (5 × 10^5 N)

t = time (20 s)

m = mass of the rocket (2 × 10^4 kg)

Δv = change in velocity (final velocity - initial velocity)

Since the rocket starts from rest, the initial velocity is 0. Therefore, Δv = final velocity.

Rearranging the equation to solve for Δv, we get:

Δv = F × t / m

= (5 × 10^5 N) × (20 s) / (2 × 10^4 kg)

= 500 m/s

Explanation

Explanation

1/f = 1/v - 1/u

2.5 = 1/0.75 - 1/u

u = -0.26 m

So, the new near point is indeed:

0.26 m

Explanation

Explanation

Magnetization (M) is the product of the magnetic field intensity (H) and the magnetic susceptibility (χ):

M = χH

Given:

χ = 3.7 × 10^-3

H = 10^4 A/m

M = (3.7 × 10^-3) × (10^4 A/m)

= 37 A/m

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

• The Indus Waters Treaty, signed on September 19, 1960, between India and Pakistan and brokered by the World Bank.
• It allocates the Western Rivers (Indus, Jhelum, Chenab) to Pakistan and the Eastern Rivers (Ravi, Beas, Sutlej) to India.
• It was signed in Karachi by Pakistan President Ayub Khan, Indian Prime Minister Jawaharlal Nehru, and Mr. W.A.B. Illif. 
• The Treaty became effective on April 1, 1960.

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