Question

The masses of two bodies are in ratio 5 : 6 and their velocities are in ratio 1:2. Then their linear momentum will be in the ratio
A. 5:06
B. 12:05
C. 1:02
D. 5:12​

Answer 1

Answer:

D.5:12 is correct answer

Answer 2

Given :-

Ratio of the masses of the two bodies = 5 : 6

Ratio of the velocities of the two bodies = 1 : 2

To Find :-

The ratio of linear momentum of the two bodies.

Analysis :-

Here we are given with the mass and the velocity of the two bodies in the form of ratios.

Firstly, convert the two ratios to fractions.

in order to find their linear momentum substitute the values accordingly such that momentum is equal to mass multiplied by the velocity of the two bodies.

Solution :-

p = Momentum

m = Mass

v = Velocity

Given that,

Ratio of masses = 5 : 6

Ratio of velocities = 1 : 2

Converting to fractions,

m₁/m₂ = 5/6

v₁/v₂ = 1/2

Using the formula,

$\underline{\boxed{\sf Momentum=Mass \times Velocity}}$

Given that,

Mass (m) = 5/6

Velocity (v) = 1/2

Substituting their values,

⇒ p = mv

⇒ p = (5/6) × (1/2)

⇒ (5 × 1) / (6 × 2)

⇒ 5/12 = 5 : 12

Therefore, the ratio of linear momentum of the two bodies is (d) 5 : 12.

Additional knowledge :-

Linear momentum:

➝ Linear momentum is defined as the vector quantity. A body’s momentum is always in the same direction as its velocity vector.

The SI unit of linear momentum is kg m/s.

Formula: Momentum = Mass × Velocity

Where,

➡ M = Mass

➡ P = Momentum

➡ V = Velocity