Assertion: A uniform elastic rod lying on smooth horizontal surface is pulled by a constant horizontal force of magnitude F as shown in the figure. Another identical elastic rod is pulled vertically upwards by a constant vertical force of magnitude F as shown in the figure . the extensions in both the rods will be same.
Reason : In a uniform elastic rod, the extension depends only on forces acting at the ends of rods.

Options

A. (a) If both Assertion and Reason are true and the Reason is correctn explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Answer

C

Explanation

Case I `F = ma rArr a = F/m `
`F-T = m'a = m/Lxa`
`T = F-m/lx.F/m = F(1-x/L)` .....(i)
Casae II `F - mg = ma'`
`a'=F/m-g`
`F-T-m'g = m'a'`
`F-T - m'g = m' (F/m-g)`
`F-T = m'.F/m`
`F-T = m/L x.F/m = x/LF`
`T = F(1-x/L)` ....(ii) Tension at a point on the rod (of length L ) at a distance `x ` from point of application of force is same in both cases . [ from Eqs. (i) and (iii) ]
Hence, weight has no effect on tension in case (ii).
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