\(m\) દળનો એક ગતિમાન બ્લોક બીજા એક \(4m\) દળના સ્થિર બ્લોક સાથે અથડાય છે. અથડામણ બાદ હલકો બ્લોક સ્થિર થાય છે. જો હલકા બ્લોકનો પ્રારંભિક વેગ \(v\) હોય, તો પુન:સ્થાપક ગુણાંક \((e) \) નું મૂલ્ય કેટલું હશે?

A \(0.5\)
B \(0.25\)
C \(0.4\)
D \(0.8\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(0.25\)

Step-by-step Solution

Detailed explanation

Let final velocity of the block of
mass \( 4 m = v'\)
Initial velocity of block of mass \( 4 m = 0 \)
Final velocity of block of mass \( m = 0\)
According to law of conservation of
linear momentum \(\begin{gathered}
mv + 4m \times 0 = 4mv' + 0 \Rightarrow v' = v/4 \hfill \\
Coefficient\,of\,restitution, \hfill \\
e = \frac{{\operatorname{Re} letive\,velocity\,of\,separation}}{{\operatorname{Re} letive\,velocity\,of\,separation}} \hfill \\
\,\,\, = \,\frac{{v/4}}{v} = 0.25 \hfill \\
\end{gathered} \)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From NEET

Explore more questions on app