Explanation

Kinetic energy formula = 1/2 × mass × velocity²  

Mass is constant.

If KE doubles, then velocity² must double.  

If velocity² becomes 2 times, velocity becomes √2 times.

So kinetic energy doubles by doubling √2 × velocity.

Last verified on 17-06-2026

Explanation

• Lenz’s law is based on the law of conservation of energy.
• It states that induced current always opposes the change causing it.
• This opposition prevents creation of energy from nothing.
• It ensures energy is neither created nor destroyed.

Last verified on 17-06-2026

Explanation

• At the center of the Earth, g = 0.
• Gravity from all directions cancels out at the center.
• So net gravitational force becomes zero.
• An object would feel weightless there.
• This is due to symmetrical distribution of Earth's mass.
• Earth’s surface gravity: 9.8 m/s²

Last verified on 17-06-2026

Explanation

• The dimension of velocity is [L T⁻¹].
• Velocity is defined as displacement per unit time.
• It shows how fast and in which direction an object moves.
• It is a vector quantity.
• SI unit of velocity is m/s.

Last verified on 17-06-2026

Explanation

1 year = 365 days (non-leap)

Seconds in 1 year = 365 × 24 × 60 × 60 = 31,536,000

For 2 years = 31,536,000 × 2 = 63,072,000

Last verified on 17-06-2026

Explanation

Let old average after 9 innings = A  

Total runs after 9 innings = 9 × A

After 10th inning he scores 100  

New average = A + 8  

New total runs = 10 × (A + 8)

So: 9A + 100 = 10(A + 8)  

9A + 100 = 10A + 80  

100 - 80 = 10A - 9A  

20 = A

Old average = 20  

New average = 20 + 8 = 28

Last verified on 17-06-2026

Explanation

Given:

AB = 5 cm

AC = 4 cm ⇒ BC = 1 cm

AC increases by 6%:

New AC = 4 × 1.06 = 4.24 cm

So new BC = 5 − 4.24 = 0.76 cm

Original BC = 1 cm

Change = 1 − 0.76 = 0.24 decrease

% change = (0.24 / 1) × 100 = 24% decrease

Last verified on 17-06-2026

Explanation

Matrix multiplication is Associative → (AB)C = A(BC)

Last verified on 17-06-2026

Explanation

The identity matrix has all diagonal elements as 1 and is full rank.

All its rows/columns are linearly independent.

Therefore, a 3 × 3 identity matrix has rank 3.

Last verified on 17-06-2026

Explanation

Equal slopes mean the points lie on the same straight line.

If AB and BC have the same slope, they form one continuous line.

Therefore, A, B, and C are collinear.

Last verified on 17-06-2026