Assertion :Two simple harmonic motions are given by $y_{1} = 10 sin (3 π t + \frac{π}{4})$ and $y_{2} = 5 sin 3 π t + \sqrt{3} cos 3 π t$ These have amplitudes in the ratio $1 : 1.$
Reason : $y_{2}$ represents two simple harmonic motions each of amplitude $5$ and so total amplitude is $10$ , same as that of $y_{1}$

Assertion and Reason are correct and Reason is the correct explanation of Assertion

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Assertion and Reason are correct but Reason is not correct explanation of A

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Both Assertion and reason are wrong

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Assertion is correct but reason is incorrect.

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Solution

The correct option is C Both Assertion and reason are wrong
$A_{1} = 10 A_{2} = \sqrt{{(5)}^{2} + {(\sqrt{3})}^{2}} = \sqrt{28} = 2 \sqrt{7} \Rightarrow \frac{A_{1}}{A_{2}} = \frac{5}{\sqrt{7}}$
so both assertion and reason statements are wrong.

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Similar questions

Q. Two simple harmonic motions are represented by the equations

y_{1} = 10 sin (3 π t + π / 4)

and

y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

. Their amplitudes are in the ratio of _________.

Q. Two simple harmonic motions are represented by the equations

Y_{1} = 10 sin (3 π t + \frac{π}{4})

and

Y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

Their amplitudes are in the ratio of;

Assertion (A) Rate constant determined from Arrhenius equation are fairly accurate for simple as well as complex molecules.

Reason (R) Reactant molecules undergo chemical change irrespective of their orientation during collision.

(a) Both assertion and reason are correct and the reason is correct explanation of assertion
(b) Both assertion and reason are correct, but reason does not explain assertion.
(c) Assertion is correct, but reason is incorrect
(d) Both assertion and reason are incorrect
(e) Assertion is incorrect but reason is correct.

Q. Assertion : Two electrons of helium atom are placed in only one shell but three electrons of lithium need two shells.
Reason: A shell can have maximum

{2n}^{2}

electrons.

Q. Assertion (A)
If the points A(8, 1), B(k, −4) and C(2, −5) are collinear, then k = 4.

Reason (R)
Three points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are collinear only when x₁(y₂− y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) = 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Assertion :Two simple harmonic motions are given by y1=10sin(3πt+π4) andy2=5sin3πt+√3cos3πt These have amplitudes in the ratio 1:1. Reason : y2 represents two simple harmonic motions each of amplitude 5 and so total amplitude is 10, same as that of y1

The correct option is C Both Assertion and reason are wrongA1=10A2=√(5)2+(√3)2=√28=2√7⇒A1A2=5√7so both assertion and reason statements are wrong.

The correct option is C Both Assertion and reason are wrong
$A_{1} = 10 A_{2} = \sqrt{{(5)}^{2} + {(\sqrt{3})}^{2}} = \sqrt{28} = 2 \sqrt{7} \Rightarrow \frac{A_{1}}{A_{2}} = \frac{5}{\sqrt{7}}$
so both assertion and reason statements are wrong.