Explanation

• Newton's law of gravitation explains the gravitational force between Earth and an object.
• The gravitational force is given by F = GMm / R^2, where M is Earth's mass, m is the object's mass, and R is Earth's radius.
• By equating gravitational force with the object's weight, F = mg, Earth's mass can be calculated using M = gR^2 / G.
• The approximate mass of Earth is 5.97 x 10^24 kg.

Last verified on 26-10-2026

Explanation

• A force in a three-dimensional Cartesian coordinate system has three perpendicular components: X, Y, and Z.
• These components act along three mutually perpendicular axes.

Additional information:

• In a two-dimensional coordinate system, a force has only two perpendicular components: X and Y.

Last verified on 26-10-2026

Explanation

Given:

F = 200 N

m = 20 kg

u = 0 m/s (from rest)

v = 50 m/s

Formula: Work done = Change in Kinetic Energy

F _ s = 1/2 _ m _ v^2

200 _ s = 1/2 _ 20 _ 50 _ 50

200 _ s = 10 _ 2500

200 _ s = 25000

s = 25000 / 200

s = 125 m

Last verified on 26-10-2026

Explanation

• The First Law of Thermodynamics states that energy can neither be created nor destroyed, only transformed from one form to another.
• Hence, it is essentially the law of conservation of energy.

Last verified on 26-10-2026

Explanation

Formula: Total Charge Q = C_eq × V

Q = 20μF × 100V

Q = 20 × 10^-6 × 100

Q = 2000 × 10^-6

Q = 2 × 10^-3 C

Last verified on 26-10-2026

Explanation

e = L _ (ΔI / Δt)

ΔI = 8 - 0 = 8 A

Δt = 0.2 s

e = 160 V

160 = L _ (8 / 0.2)

160 = L * 40

L = 160 / 40 = 4 H

Last verified on 26-10-2026

Explanation

Force on charge: F = q(v x B)

If v is perpendicular to B (90°), force is always perpendicular to velocity, acting as centripetal force.

If v perpendicular to B: Circle

If v at some angle to B: Helix

If v parallel to B: Straight line

Last verified on 26-10-2026

Explanation

In SHM:

Total Energy = KE + PE = constant

At extreme positions:

Velocity = 0, so KE = 0

So PE = Total Energy

Therefore PE is maximum at extremes, and KE is maximum at mean position.

Last verified on 26-10-2026

Explanation

Formula: KE = p^2 / 2m

p = 10 Ns

m = 5 kg

KE = 10^2 / (2 x 5)

KE = 100 / 10

KE = 10 J

Last verified on 26-10-2026

Explanation

Closed pipe fundamental: f_closed = v / 4L

Closed pipe 1st overtone = 3rd harmonic = 3 x v / 4L

Open pipe fundamental: f_open = v / 2L

Divide: (3v/4L) / (v/2L) = 3/2 = 1.5

So closed 1st overtone = 1.5 x f_open

Last verified on 26-10-2026