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If the sum of two unit vectors is a unit vector, then the magnitude of the difference is

1) √2 2) √3 3) 1/√2 4) √5 Answer: 2) √3 Solution: Let be the two unit... View Article

A man crosses a 320 m wide river perpendicular to the current in 4 mm. If in still water he can swim with a speed 5/3 times that of the current, then the speed of the current, in m/min is

1) 30 2) 40 3) 50 4) 60 Answer: 4) 60 Solution: Width of the river, d = 320 m Speed of man, v = (5/3)u Speed of current = u u = 60 m/min... View Article

The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is at 90o with a force of smaller magnitude, what are the magnitudes of forces?

1) 2, 5 2) 14, 4 3) 5, 13 4) 10, 8 Answer: 3) 5, 13 Solution: Let P be the smaller force and Q be the greater force. Then P+Q=18... View Article

Surface area is

Surface area is 1) Scalar 2) Vector 3) Neither scalar nor vector 4) Both scalar and vector Answer: 1) Scalar Solution: Surface area... View Article

A steam boat goes across a lake and comes back

A steam boat goes across a lake and comes back (a) On a quite day when the water is still and (b) On a rough day when there is uniform air... View Article

Sound travels through a gas under which of the following condition?

a) Isothermal conditionb) Non-isothermal conditionc) Adiabatic conditiond) Transverse conditionSolution: c) Adiabatic conditionWhen sound travels... View Article

What are the essential properties a medium must possess for the propagation of mechanical waves?

a) Stable pressureb) Maximum frictionc) Constant temperatured) Minimum frictionSolution: d) Minimum frictionThe friction force amongst the... View Article

When a pebble is dropped into a pond of still water, what happens?

a) Particles moveb) Waves movec) The pebble movesd) Water movesSolution: b) Waves moveWhen a pebble is thrown in still water, a circular pattern... View Article

A string of mass 3 kg is under tension of 400 N. the length of the stretched string is 25 cm. If the transverse jerk is stuck at tone end of the string how long does the disturbance take to reach the other end?

(a) 25 π2ms-2(b) 5 π2ms-2(c) -5 π2ms-2(d) -25 π2ms-2Solution: (c) -5 π2ms-2We know, ω = 2 π/T = 2 π/0.2 = 10 π rad... View Article

With propagation of longitudinal waves through a medium, the quantity transmitted is

(a) matter(b) energy(c) energy and matter(d) energy, matter and momentumSolution: (b) energyLongitudinal waves are propagated by propagation of... View Article

A metallic wire of 1 m length has a mass of 10 × 10^-3 kg. If a tension of 100 N is applied to a wire, what is the speed of the transverse wave?

(a) 10 ms-1 (b) 0.1 ms-1 (c) 100 ms-1 (d) 200 ms-1 Solution: (c) 100 ms-1 Linear mass density is defined as measure of mass per unit of length,... View Article

A 40 cm wire having a mass of 3.2 g is stretched between two fixed supports 40.05 cm apart. In its fundamental mode, the wire vibrates at 220 Hz. If the area of cross section of the wire is 1.0 mm², find its Young modulus.

Strain = ΔI/I = 0.125 x 10-2 and f = 1/2L √(T/m)=> T = 248.19 NNow, stress = Tension/Area = 248.19 x 106Therefore, Young modulus =... View Article

The equation of a standing wave, produced on a string fixed at both ends, is

Question: The equation of a standing wave, produced on a string fixed at both ends, isy = (0.4 cm) sin(0.314 cm−1)x] cos[(600π s−1)t].What could... View Article

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by

y = (0.4 cm) sin[(0.314 cm−1)x] cos[(600π s−1)t](a) What is the frequency of vibration? (b) What are the positions of the nodes? (c) What is the... View Article

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s⁻¹ and amplitude is 0.5 cm.

(a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the... View Article

A string of length L fixed at both ends vibrates in its fundamental mode at a frequency v and a maximum amplitude A.

(a) Find the wavelength and the wave number k. (b) Take the origin at one end of the string and the X-axis along the string. Take the Y-axis... View Article

Figure shows an aluminium wire of length 60 cm joined to the steel wire of length 80 cm and stretched between two fixed supports.

Question: Figure (below) shows an aluminium wire of length 60 cm joined to the steel wire of length 80 cm and stretched between two fixed... View Article

A uniform horizontal rod of length 40 cm and mass 1.2 kg is supported by two identical wires as shown in figure

Question: A uniform horizontal rod of length 40 cm and mass 1.2 kg is supported by two identical wires as shown in figure (below). Where should a... View Article

Two wires are kept right between the same pair of supports. The tensions in the wires are in the ratio 2:1, the radii are in the ratio 3:1 and the densities are in the ratio 1 : 2. Find the ratio of their fundamental frequencies.

The ratio of mass per unit length of the wires:ρ1/ρ2 x r12/r22 = (1/2) x (9/1)= 9/2Fundamental frequency of wire = (1/2l) √(T/μ)Thus, f1/f2 = 2:3... View Article

Three resonant frequencies of the string are 90, 150 and 210 Hz.

(a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given... View Article