A uniform electric field, E→=-4003j^NC-1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 210×106ms-1. This particle is aimed to hit a target T, which is5m away from its entry point into the field as shown schematically in the figure. Take qm=1010Ckg-1. Then

(C) time taken by the particle to hit T could be 56μs as well as 52μs

(A) the particle will hit T if projected at an angle 45° from the horizontal

(B) the particle will hit T if projected either at an angle 30° or 60° from the horizontal

(C) time taken by the particle to hit T could be 56μs as well as 52μs

(D) time taken by the particle to hit T is 53μs

JEE Advanced · Physics · 4. Motion in 2D

A uniform electric field, $\vec{E} = - 400 \sqrt{3} \hat{j} N C^{- 1}$ is applied in a region. A charged particle of mass $m$ carrying positive charge $q$ is projected in this region with an initial speed of $2 \sqrt{10} \times 10^{6} m s^{- 1}$ . This particle is aimed to hit a target $T$ , which is $5 m$ away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m} = 10^{10} C {kg}^{- 1}$ . Then

A the particle will hit $T$ if projected at an angle $45 °$ from the horizontal
B the particle will hit $T$ if projected either at an angle $30 °$ or $60 °$ from the horizontal
C time taken by the particle to hit $T$ could be $\sqrt{\frac{5}{6}} μ s$ as well as $\sqrt{\frac{5}{2}} μ s$
D time taken by the particle to hit $T$ is $\sqrt{\frac{5}{3}} μ s$

Verified Solution

Answer & Solution

Correct Answer

(C) time taken by the particle to hit $T$ could be $\sqrt{\frac{5}{6}} μ s$ as well as $\sqrt{\frac{5}{2}} μ s$

Step-by-step Solution

Detailed explanation

a_{y} = \frac{E}{M} = 4 \sqrt{3} \times 10^{12} m s^{2}

R = \frac{u^{2} \sin 2 θ}{a_{y}}

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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From JEE Advanced

Match the chemical substance in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.

Column I	Column II
A. $C _6 H _5 CHO$	p. Gives precipitate with 2, 4-dinitrophenylhydrazine
B. $CH _3 \equiv CH$	q. Gives precipitate with $AgNO _3$
C. $CN ^{-}$	r. Is a nucleophile
D. $I ^{-}$	s. Is involved in cyanohydrin formation

JEE Advanced 2007 Medium

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Column I	Column II
A. \(C _6 H _5 CHO\)	p. Gives precipitate with 2, 4-dinitrophenylhydrazine
B. \(CH _3 \equiv CH\)	q. Gives precipitate with \(AgNO _3\)
C. \(CN ^{-}\)	r. Is a nucleophile
D. \(I ^{-}\)	s. Is involved in cyanohydrin formation