\('m'\) દળ અને \(d _{1}\) ઘનતા ઘરાવતા નાના બોલને જ્યારે ગ્લીસરીન ભરેલા એક પાત્રમાં મુક્ત કરવામાં આવે છે તો અમુક સમય બાદ તેનો વેગ અચળ થઈ જાય છે. જો ગ્લીસરીનની ઘનતા \(d _{2}\) હોય તો બોલ ઉપર પ્રવર્તતું સ્નિગ્ધ બળ ........ હશે.

A \(m g\left(1-\frac{d_{1}}{d_{2}}\right)\)
B \(m g\left(1-\frac{d_{2}}{d_{1}}\right)\)
C \(m g\left(\frac{d_{1}}{d_{2}}-1\right)\)
D \(m g\left(\frac{d_{2}}{d_{1}}-1\right)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(m g\left(1-\frac{d_{2}}{d_{1}}\right)\)

Step-by-step Solution

Detailed explanation

\(F_{V}=m g-F_{B}\) \(=m g-\left(\frac{m}{d_{1}} \times d_{2}\right) g\) \(=m g\left(1-\frac{d_{2}}{d_{1}}\right)\)

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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