An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will be

A \(v =4 \hat{ i }\,m / s , a =8 \hat{ j }\,m / s ^2\)
B \(v =4 \hat{ j }\,m / s , a =8 \hat{ i }\,m / s ^2\)
C \(v =-4 \hat{ j }\,m / s , a =8 \hat{ i }\,m / s ^2\)
D \(v =-4 \hat{ i }\,m / s , a =-8 \hat{ j }\,m / s ^2\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(v =4 \hat{ j }\,m / s , a =8 \hat{ i }\,m / s ^2\)

Step-by-step Solution

Detailed explanation

\(a _{ c }=\frac{ V ^2}{ r }=\frac{4^2}{2}=\frac{16}{2}=8\,m / s ^2\) \(\overrightarrow{ V }=4 \hat{ j }\) \(\rightarrow a _{ c }=8 \hat{ i }\)

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

Match List \(I\) (Wavelength range of electromagnetic spectrum) with List \(II\) (Method of production of these waves) and select the correct option from the options given below the lists

List \(I\)	List \(II\)
\((1)\) \(700\, nm\) to \(1\,mm\)	\((i)\) Vibration of atoms and molecules
\((2)\) \(1\,nm\) to \(400\, nm\)	\((ii)\) Inner shell electrons in atoms moving from one energy level to a lower level
\((3)\) \( < 10^{-3}\,nm\)	\((iii)\) Radioactive decay of the nucleus
\((4)\) \(1\,mm\) to \(0.1\,m\)	\((iv)\) Magnetron valve

JEE Mains 2014 Medium

Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) )

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