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The angle between the two vectors [latex]vec{A}=5hat{i}+5hat{j}[/latex] and [latex]vec{B}=5hat{i}-5hat{j}[/latex] will be

1) zero 2) 450 3) 900 4) 1800 Answer: 3) 900 Solution: \(\begin{array}{l}\vec{A}.\vec{B}=(5\hat{i}+5\hat{j}).(5\hat{i}-5\hat{j})=0\end{array} \) Therefore, θ = 900

A force [latex]vec{F}=5hat{i}+6hat{j}+4hat{k}[/latex] acting on a body, produces displacement [latex]vec{S}=6hat{i}-5hat{k}[/latex]. Work done by the force is

1) 10 units 2) 18 units 3) 11 units 4) 5 units Answer: 1) 10 units Solution: \(\begin{array}{l}W = \vec{F}.\vec{S}= (5\hat{i}+6\hat{j}+4\hat{k})(6\hat{i}-5\hat{k})=... View Article

If [latex](vec{P}.vec{Q}) = PQ[/latex], then angle between [latex]vec{P}[/latex] and [latex]vec{Q}[/latex] is

1) 0⁰

2) 300 3) 450 4) 600 Answer: 1) 00 Solution: \(\begin{array}{l}cos\theta =\frac{\vec{P}.\vec{Q}}{PQ}=1\end{array} \) Therefore, θ = 00

If [latex]\vec{A}\times \vec{B}=\vec{C}[/latex], then which of the following is wrong

1) \(\begin{array}{l}\vec{C}\perp \vec{A}\end{array} \) 2) \(\begin{array}{l}\vec{C}\perp \vec{B}\end{array} \) 3) \(\begin{array}{l}\vec{C}\perp (\vec{A}+\vec{B})\end{array} \) 4) \(\begin{array}{l}\vec{C}\perp (\vec{A}\times \vec{B})\end{array} \) Answer: 4) \(\begin{array}{l}\vec{C}\perp (\vec{A}\times \vec{B})\end{array} \) Solution: From the... View Article

The angle between the vectors [latex]vec{A}[/latex] and [latex]vec{B}[/latex] is θ. The value of triple product [latex]vec{A}(vec{A}times vec{B})[/latex] is

1) A2B 2) Zero 3) A2B sin θ 4) A2B cos θ Answer: 2) Zero Solution: Let \(\begin{array}{l}\vec{A}(\vec{A}\times \vec{B}) = \vec{A}.\vec{C}\end{array} \) Here \(\begin{array}{l}\vec{C}=\vec{B}\times \vec{A}\end{array} \).... View Article

If for two vectors [latex]vec{A}[/latex] and [latex]vec{B}[/latex], sum [latex](vec{A}+vec{B})[/latex] is perpendicular to the difference [latex](vec{A}-vec{B})[/latex]. The ratio of their magnitude is

1) 1 2) 2 3) 3 4) None of these Answer: 1) 1 Solution: The sum \(\begin{array}{l}(\vec{A}+\vec{B})\end{array} \) is perpendicular to the... View Article

A body is moving with velocity 30 m/s towards east, After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is

1) 5 m/s2 2) 1 m/s2 3) 7 m/s2 4) √7 m/s2 Answer: 1) 5 m/s2 Average acceleration \(\begin{array}{l}\vec{A_{avg}}= \frac{(\vec{v_{f})-\vec{v_{i}}}}{t}=\frac{40\hat{j}-30\hat{i}}{10}\end{array} \) \(\begin{array}{l}\vec{A_{avg}}= \sqrt{40^{2}+30^{2}}/10\end{array}... View Article

A body moves due East with velocity 20 km/hour and then due North with velocity 15 km/hour. The resultant velocity

1) 5 km/hour 2) 15 km/hour 3) 20 km/hour 4) 25 km/hour Answer: 4) 25 km/hour Solution: \(\begin{array}{l}Resultant velocity = \sqrt{20^{2}+15^{2}}\end{array}... View Article

Two forces, F₁ and F₂are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is

1) cos–1(1 / 2) 2) cos–1 (–1 / 2) 3) cos–1 (–1 / 4) 4) cos–1 (1 / 4) Answer: 3)... View Article

Two vectors [latex]vec{A}[/latex] and [latex]vec{B}[/latex] are such that [latex]vec{A}+vec{B}=vec{A}-vec{B}[/latex]. Then

Two vectors \(\begin{array}{l}\vec{A}\end{array} \) and \(\begin{array}{l}\vec{B}\end{array} \) are such that \(\begin{array}{l}\vec{A}+\vec{B}=\vec{A}-\vec{B}\end{array} \). Then 1) \(\begin{array}{l}\vec{A}.\vec{B}= 0\end{array} \) 2) \(\begin{array}{l}\vec{A} \times \vec{B}= 0\end{array} \) 3) \(\begin{array}{l}\vec{A} =... View Article

What is the angle between [latex]vec{P}[/latex] and the resultant of [latex](vec{P}+vec{Q})[/latex] and [latex](vec{P}-vec{Q})[/latex]?

What is the angle between \(\begin{array}{l}\vec{P}\end{array} \) and the resultant of \(\begin{array}{l}(\vec{P}+\vec{Q})\end{array} \) and \(\begin{array}{l}(\vec{P}-\vec{Q})\end{array} \)? 1) Zero 2) tan-1 (P/Q) 3) tan-1(Q/P)... View Article

Which pair of the following forces will never give (c) 2 N and 2 N (c) 1 N and 3 N resultant force of 2 N

1) 2 N and 2 N 2) 1N and 1 N 3) 1 N and 3 N 4) N and... View Article

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in the air is 340 m/s.

(a) 6 (b) 4 (c) 12 (d) 8 Solution Fundamental frequency of the closed organ pipe is f = v/4L... View Article

Three sound waves of equal amplitudes have frequencies(f-1, f, f+1). They superpose to give beats. The number of beats produced per second is

(a) 2 (b) 1 (c)4 (d) 3 Solution Beat produced between(f-1) and f is 1. Beat produced between f and... View Article

A person standing on an open ground hears the sound of a jet aeroplane, coming from the north at an angle 60⁰ with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, the speed of the plane is

(a)(√3/2) v (b)2v/√3 (c) V (d) v/2 Solution Distance, PQ = vp x t (Distance = speed x time) Distance... View Article

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving at a speed of 20 m/s with respect to the ground. If an observer in car A detects a frequency of 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B? (speed of sound in air = 340 m/s)

(a)2250 Hz (b)200 Hz (c)2300 Hz (d)2150 Hz Solution f’ = f{(v – v0)/(v + vs)} 2000 = f{(340 –... View Article

A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? (Given reference intensity of sound is 10^-12 W/m²)

(a) 40 cm (b) 20 cm (c) 10 cm (d) 30 cm Solution Using β = 10 log10(I/I0) Or 120... View Article

A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in the air

Question: A resonance tube is old and has a jagged end. It is still used in the laboratory to determine... View Article

Two sources of sound S₁ and S₂ produce sound waves of the same frequency 660 Hz. A listener is moving from source S₁ towards S₂ with constant speed u m/s and he hears 10 beats. The velocity of sound is 330 m/s. Then u is equals

(a)5.5 m/s (b) 15.0 m/s (c)2.5 m/s (d) 10.0 m/s Solution f1 = f[(v – v0)/v] f2 = f[(v +... View Article

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source when it is moving away from the observer after crossing him? (Take the velocity of sound in air as 350 m/s)

(a) 750 Hz (b) 857 Hz (c) 1143 Hz (d) 807 Hz Solution When source is moving towards a stationary... View Article

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