એક બલૂન \(10\; m/s\) ના અચળ વેગથી ઉપર તરફ ગતિ કરે છે. જ્યારે તે જમીનની સપાટીથી \(75\) મીટરની ઉંચાઈ પર હોય, ત્યારે બલૂનમાંથી સીમિત દળનો પદાર્થ છોડવામાં આવે છે. જ્યારે પદાર્થ જમીન સાથે અથડાય ત્યારે જમીનથી બલૂનની ઊંચાઈ (\(m\) માં) કેટલી હશે? (\(g=10 \,{m} / {s}^{2}\) લો)

A \(125\)
B \(250\)
C \(300\)
D \(200\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(125\)

Step-by-step Solution

Detailed explanation

\(S=u t+\frac{1}{2} a t^2\) \(-75=+10 t+\frac{1}{2}(-10) t^2\) \(\Rightarrow t=5 sec\) Object takes \(t=5 s\) to fall on ground Height of balloon from ground \(H=75+u t\) \(H=75+10 \times 5=125 m\)

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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