JEE Mains · Physics · STD 11- 8. mechanical properties of solids

A steel wire of length \(3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)\) and a copper wire of length \(4.4\,M\) \(\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)\), both of radius \(1.4\,mm\) are connected end to end. When stretched by a load, the net elongation is found to be \(1.4\,mm\). The load applied, in Newton, will be. (Given \(\pi=\frac{22}{7}\))

A \(360\)
B \(180\)
C \(1080\)
D \(154\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(154\)

Step-by-step Solution

Detailed explanation

\(\Delta \ell_{1}+\Delta \ell_{2}=\Delta \ell\) \(\frac{ F \ell_{1}}{ A _{1} y _{1}}+\frac{ F \ell_{2}}{ A _{2} y _{2}}=\Delta \ell\) \(F =\frac{\Delta \ell}{\frac{\ell_{1}}{ A _{1} y _{1}}+\frac{\ell_{2}}{ A _{2} y _{2}}}=1.54 \times 10^{2}=154\)

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.

Same subject

A concave mirror has radius of curvature of \(40\, cm\). It is at the bottom of a glass that has water filled up to \(5\, cm\) (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance \(d\) from the surface of water. The value of \(d\) is close to ......\(cm\) (Refractive index of water \(= 1.33\))

JEE Mains 2019 Hard

List-\(I\)	List-\(II\)
\((a)\) \(MI\) of the rod (length \({L}\), Mass \({M}\), about an axis \(\perp\) to the rod passing through the midpoint)	\((i)\;\frac {8 {ML}^{2}}{3}\)
\((b)\) MI of the rod (length \(L\), Mass \(2 M\), about an axis \(\perp\) to the rod Passing through one its end)	\((ii)\;\frac {{ML}^{2}}{3}\)
\((c)\) MI of the rod (length \(2 {L}\), Mass \({M}\), about an axis \(\perp\) to the rod Passing through its midpoint)	\((iii)\;\frac {{ML}^{2}}{12}\)
\((d)\) MI of the rod (length \(2 {L}\), Mass \(2 {M}\), about an axis \(\perp\) to the rod passing through one of its end)	\((iv)\;\frac {2 {ML}^{2}}{3}\)

Choose the correct answer from the options given below

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