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MHT CET202613 April 2026Evening ShiftPhysicsMathematics in PhysicsActual

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. Length of cylinder is 8.0 cm and radius is 4.0 cm. Find the percentage error in the calculated value of the volume.

Options

  1. A1.25 %
  2. B1.75 %
  3. C1.5 %
  4. D2.75 %

Correct answer

C. 1.5 %

Step-by-step solution

The volume of a cylinder is given by V = R^2 L . Since the diameter D is measured, we can write the volume in terms of diameter as V = D^2 L 4 . The maximum percentage error in the volume is given by: V V 100 = ( 2 D D + L L ) 100 Given values: Length of the cylinder, L = 8.0 cm Least count of meter rod, L = 0.1 cm Radius of the cylinder, R = 4.0 cm Diameter, D = 2R = 8.0 cm Least count of vernier calipers, D = 0.01 cm Substituting these values into the percentage error formula: V V 100 = ( 2 0.01 8.0 + 0.1 8.0 ) 1

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