Question

A body A with a mass of 100g is moving with a velocity of 10cm/s. A body B with a mass of 1kg is moving with a velocity of 1m/s. What is the ratio of momentum for A to B?

Answer 1

Answer:

momentum is multiple of mass and velocity so  

mass of object in kg is 0.1kg

momentum = 1.5 kg m/s

Answer 2

Answer:

1 : 100

Explanation:

As per the provided information in the given question, we have :

• Mass of the object A = 100g
• Velocity of the object A = 10 cm/s
• Mass of the object B = 1 kg
• Velocity of the object B = 1 m/s

We've been asked to calculate the ratio of momentum for A to B.

In order to calculate the ratio of momentum for A to B, firstly we need to find the momentum of both object A and object B.

Momentum of object A :

• Mass of the object A = 100g ⇒ 0.1 kg
• Velocity of the object A = 10 cm/s ⇒ 0.1 m/s

Momentum is the product of mass and velocity.

$\longrightarrow \sf{\quad { p = mv}}$

• p denotes momentum
• m denotes mass
• v denotes velocity

$\longrightarrow \sf{\quad { p_{A} = 0.1 \; kg \times 0.1 \; ms^{-1}}}$

$\longrightarrow \quad \underline{\boxed{\sf{ p_{A} = 0.01 \; kg.ms^{-1}}}}$

Now,

Momentum of object B :

• Mass of the object B = 1 kg
• Velocity of the object B = 1 m/s

Momentum is the product of mass and velocity.

$\longrightarrow \sf{\quad { p = mv}}$

• p denotes momentum
• m denotes mass
• v denotes velocity

$\longrightarrow \sf{\quad { p_{B} = 1 \; kg \times 1 \; ms^{-1}}}$

$\longrightarrow \quad \underline{\boxed{\sf{ p_{B} = 1 \; kg.ms^{-1}}}}$

Now, we have to find the ratio. Ratio will be given by,

$\longrightarrow \sf{\quad { Ratio = p_{A} \ratio p_{B} }}$

$\longrightarrow \sf{\quad { Ratio =\dfrac{ p_{A}}{p_{B}} }}$

$\longrightarrow \sf{\quad { Ratio =\dfrac{ 0.01 \; kg.ms^{-1}}{1 \; kg.ms^{-1}} }}$

$\longrightarrow \sf{\quad { Ratio =\dfrac{ 1 }{100} }}$

$\longrightarrow \quad \underline{\boxed{\pmb{ \frak{Ratio = 1 : 100} }}}$

Therefore, the ratio of momentum for A to B is 1 : 100.