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The resultant of the two vectors having magnitude 2 and 3 is 1. What is their cross product?

1) 6 2) 3 3) 1 4) 0 Answer: 4) 0 Solution: 1-4-9 =12cosθ cosθ = -12/12 = -1 By solving we get θ =... View Article

The area of the parallelogram represented by the vectors [latex]vec{A}=(2hat{i}+3hat{j})[/latex] and [latex]vec{B}=(hat{i}+4hat{j})[/latex]

1) 14 units 2) 7.5 units 3) 10 units 4) 5 units Answer: 4) 5 units Solution:... View Article

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: Therefore, θ = 900... View Article

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:... 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: Therefore, θ = 00... View Article

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

1) 2) 3) 4) Answer: 4) Solution: From the property of vector product, which cannot be... 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 Here . Which is... 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 or Because of commutative property of dot product... 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 = 5m/sec2... 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: = = 25 km/hr... 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) cos–1 (–1 / 4) Solution: The condition given is f1 = f, f2... 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 . Then 1) 2) 3) 4) Answer: 4) Solution: It is only possible when is a null vector... 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 ? 1) Zero 2) tan-1 (P/Q) 3) tan-1(Q/P) 4) tan-1(P/Q)(P+ Q) Answer: 1) Zero Solution: Resultant ... 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 4 N Answer: 4) N and 4 N Solution: If two vectors A and B are given then the... 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) 8SolutionFundamental frequency of the closed organ pipe isf = v/4Lf = 340/(4 x 0.85) = 100 HzThe natural frequencies of the... 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) 3SolutionBeat produced between(f-1) and f is 1.Beat produced between f and f+1 is 1.Beat produced between(f-1) and (f+1) is 2∴... 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/2SolutionDistance, PQ = vp x t (Distance = speed x time)Distance , QR = V.tCos 600 = PQ/QR½ = (vp x t)/( v.t)vp=... 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 HzSolutionf’ = f{(v - v0)/(v + vs)}2000 = f{(340 - 20)/(340 + 20)}f = 2250 HzAnswer: (a) 2250 Hz... 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 cmSolutionUsing β = 10 log10(I/I0)Or 120 = 10 log 10(I/ 10-12)I/10-12 = 1012I = 1Also I = 1= P/4πr2 =... 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 the velocity of sound in the air. A... View Article