Question

Two masses of 1 g and 9 g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is

• A. 1 : 9
• B. 9 : 1
• C. 1 : 3
• D. 3 : 1

Answer 1

The Correct Option is C

\(\frac{K_1}{K_2}=\frac{p_1^2}{p_2^2} \times \frac{M_2^2}{M_1^2}\) 
when \(K_1=K_2\)
\(\frac{p_1}{p_2}=\sqrt{\frac{M_1}{M_2}}=\sqrt{\frac{1}{9}}=\frac{1}{3}\)
\(\therefore \, \, p_1 :p_2 =1 : 3\)

An object's mass times its velocity is said to have linear momentum. A vector quantity, that is. The letter "p" stands for it. A body's momentum and velocity both point in the same general direction. The overall momentum of an isolated system remains constant since momentum is a conserved quantity. Kg m/s is the SI unit for linear momentum.

Given by is the formula for a body's linear momentum.

p = m⋅v

Where,

m = the object's mass

v = the object's velocity

Now, linear momentum is calculated using the formula,

linear momentum = mass × velocity

So, the dimensional formula of linear momentum can be calculated using the above formula

 

Dimensional formula of mass = [M¹L⁰T⁰]

Dimensional formula of velocity = [M⁰L¹T^-1]

Dimensional Formula of linear momentum = [M¹L⁰T⁰] × [M⁰L¹T^-1] = [M¹L¹T^-1]

Therefore, the dimensional formula of linear momentum is [M¹L¹T^-1].