એક ઘોડેસવાર અડધું અંતર \(5\,m/s\) ની ઝડપથી કાપે છે. બાકીનો ભાગ અડધા સમય માટે \(10\,m/s\) ની ઝડપથી અને બાકીનું \(15\,m/s\) ની ઝડપ સાથે બીજા અડધા સમય સાથે કાપે છે. ગતિના કુલ સમય દરમિયાન સવારની સરેરાશ ઝડપ \(\frac{x}{7}\,m / s\) છે. \(x\) નું મૂલ્ય ........... થશે.

A \(25\)
B \(20\)
C \(26\)
D \(50\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(50\)

Step-by-step Solution

Detailed explanation

\(t _{ AB }=\frac{ x }{5 m / s }\) In motion \(BC\) \(x = d _1+ d _2\) where \(d _1 , d _2\) we the distance travelled with \(10\,m / s\) and \(15\,m / s\) respectively in equal time intervals \(\frac{' t^{\prime}}{2} \text { each }\) \(d_1=\frac{10 t}{2}, d_2=\frac{15 t }{2}\)…

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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\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)