એક બોલને \(t=0 \,s\) એ \(50 \,ms ^{-1}\) જેટલા પ્રારંભિક વેગ સાથે શિરોલંબ ઉર્ધ્વ દિશામાં પ્રક્ષિપ્ત કરવામાં આવે છે. \(t=2\,s\) એ બીજા બોલને સમાન વેગથી શિરોલંબ ઉર્ધ્વ દિશામાં પ્રક્ષિપ્ત કરવામાં આવે છે. \(t=\).......... \(s\) એ બીજો બોલ પ્રથમ બોલને મળશે. \(\left( g =10 \;ms ^{-2} s\right.\))

A \(6\)
B \(5\)
C \(4\)
D \(3\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(6\)

Step-by-step Solution

Detailed explanation

Let they meet at \(t = t\) So first ball gets \(t \; sec\). and \(2^{\text {nd }}\) gets \(( t -2) \; sec\) . and they will meet at same height \(h _{1}=50 t -\frac{1}{2} gt ^{2}\) \(h _{2}=50( t -2)-\frac{1}{2} g ( t -2)^{2}\) \(h _{1}= h _{2}\)…

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.

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