એક તકતી અને એક ગોળાની ત્રિજયા સમાન પણ દ્રવ્યમાન જુદા છે તે સમાન ઊંચાઇ અને લંબાઇના બે ઢાળ પરથી ગબડે છે. બેમાંથી કયો પદાર્થ તળિયે પહેલો પહોંચશે?

A ગોળો
B બંને એક જ સમયે પહોંચશે.
C તેમના દ્રવ્યમાનો પર આધાર રાખે છે.
D તકતી

Verified Solution

Answer & Solution

Correct Answer

(A) ગોળો

Step-by-step Solution

Detailed explanation

Time taken by the body to reach the bottom when it rolls down an inclined plane without slipping is given by \(t = \sqrt {\frac{{2l\left( {1 + \frac{{{k^2}}}{{{R^2}}}} \right)}}{{g\sin \theta }}} \)

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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