Question

An object flying in air with velocity $\left(20\hat{i} + 25\hat{j} - 12\hat{k}\right)$ suddenly breaks in two pieces whose masses are in the ratio $1 : 5$. The smaller mass flies off with a velocity $\left(100\hat{i} + 35\hat{j} + 8\hat{k}\right)$. The velocity of the larger piece will be :

• A. $4\hat{i} + 23\hat{j} -16\hat{k}$
• B. $-100\hat{i} + 35\hat{j} -8\hat{k}$
• C. $20\hat{i} + 15\hat{j} -80\hat{k}$
• D. $-20\hat{i} + 15\hat{j} -80\hat{k}$

Answer 1

The Correct Option is A

The correct option is(A): \(4\hat{i} + 23\hat{j} -16\hat{k}\)

Conservation of linear momentum, 
\(m \vec{v}_0 = \frac{m}{6} \vec{v}_1+ \frac{5m}{6} \vec{v}_2\)
\(\Rightarrow m( 20\hat{i} + 25\hat{j} - 12 \hat{k})\)
\(= \frac{m}{6} ( 100 \hat{i} + 35 \hat{j} + 8\hat{k}) + \frac{5m}{6} \vec{v}_2\)
\(\Rightarrow \vec{v}_2 = 4\hat{i} + 23\hat{j} - 16\hat{k}\)

The term "motion" refers to a body's change in position over time as a result of its environment. Any mass-containing object's motion in physics can be quantified in terms of distance, displacement, speed, velocity, acceleration, and time. Depending on the body's velocity, the motion can either be uniform or non-uniform. The distance a body has travelled in a unit of time is known as its speed, and the displacement in a unit of time is known as its velocity. 

Translation is the term used to describe motion along a line or a curve.

Rotation is a motion that modifies a body's orientation. 

Every motion has a frame of reference to which it is related.

A body is simply being described in relation to a frame of reference that is moving with the body while we claim it is at rest.

Some of the day-to-day motion examples are – 

• Daily activities such as walking, closing doors, running, etc.
• Air flowing in and out of the lungs.
• Automobile vehicles commuting passengers from one stop to another.
• Daily activities like, walking, running, or jumping.
• Throwing a ball