Explanation

Scalar product = AB cosθ

Magnitude of vector product = AB sinθ

For equal magnitudes:

AB cosθ = AB sinθ

cosθ = sinθ

tanθ = 1

θ = 45°

So magnitude is equal at 45°.

Last verified on 28-10-2026

Explanation

• According to Coulomb's law, the electrostatic force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.
• Doubling both charges makes the force 4 times greater, while doubling the distance makes the force 1/4 as large.
• The combined effect is 4 x 1/4 = 1. Therefore, the force remains the same.
• Coulomb's law applies to stationary point charges in a vacuum or approximately in air.

Last verified on 28-10-2026

Explanation

• An elastic collision is a collision in which both total kinetic energy and total momentum are conserved.
• Momentum is conserved in both elastic and inelastic collisions, provided the system is isolated.

Last verified on 28-10-2026

Explanation

• According to Newton's second law, acceleration equals net force divided by mass.
• If the mass doubles and the force becomes half, the new acceleration is one-fourth of the original acceleration.
• For example, if the original acceleration is 2 m/s^2, the new acceleration will be 0.5 m/s^2.

Last verified on 28-10-2026

Explanation

• The scalar product (dot product) of two vectors is given by A · B = AB cosθ.
• The scalar product is maximum when the angle between the vectors is 0°, because cos0° = 1.
• At 0°, both vectors point in the same direction, so their dot product equals AB.
• At 90°, the dot product is zero because cos90° = 0.

Last verified on 28-10-2026

Explanation

• Least count is the smallest measurement that an instrument can read or measure.
• A smaller least count generally means greater precision.
• Because the instrument can detect smaller changes in a measurement.

Last verified on 28-10-2026

Explanation

• The electronic configuration 2s¹, 2p⁵ contains six electrons in the second shell.
• This configuration is higher in energy than the ground-state configuration 2s², 2p⁴ of oxygen.
• A species in a higher-energy state may release energy when it changes to a lower-energy, more stable state.

Last verified on 27-10-2026

Explanation

• Hydrochloric acid (HCl) is a strong acid, while barium hydroxide [Ba(OH)₂] is a strong base.
• When HCl is added to Ba(OH)₂, a neutralization reaction occurs: Ba(OH)₂ + 2HCl → BaCl₂ + 2H₂O
• The final concentration of hydrogen ions depends on the relative amounts of acid and base.
• If the added acid is insufficient to neutralize all the base, hydroxide ions remain in excess.
• If enough acid is added to exceed the neutralization point, hydrogen ions become excess.

Last verified on 27-10-2026

Explanation

• Racing cars are made more stable by lowering their centre of gravity, which reduces the tendency to topple while turning.
• A lower centre of gravity helps the car maintain balance when experiencing outward effects during sharp turns.
• Racing cars also use wide tyres and carefully designed suspension systems to improve grip and stability.

Last verified on 27-10-2026

Explanation