Three sound waves of equal amplitudes have frequencies (n –1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be
no. of beats = 1 (HCF of beat frequencies
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L meter long. The length of the open pipe will be
A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is :
A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?
n = PV/RT = mass/Molarmass = PV/RT
density = mass/volume = (Molar mass)P/RT = (mNA)P/RT = mP/KT
The temperature inside a refrigerator is t2 ºC and the room temperature is t1 ºC. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be
Qmore/W = Qmore/Qmore-Qless = Tmore/Tmore-Tless = t1+273/(t1+273)-(t2+273) = t1+273/t1-t2
One mole of an ideal monatomic gas undergoes a process described by the equation PV3 = constant. The heat capacity of the gas during this process is :
PV3 = constant for a polytropic process.
PV3 = constant
C = Cv + R /1- ∝ = 3/2 R + R / 1-3 = 3R/2- R /2= R
A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be
Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100ºC, while the other one is at 0ºC. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is
Body at 100°C temperature has greater heat capacity than body at 0°C so final temperature will be closer to 100°C. So Tc > 50°C
Three liquids of densities 1, 2 and 3 (with 1 > 2 > 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ1, θ2 and θ3 obey
h = 2Tcosθ/pgr
cosθ1/p1= cosθ2/p2 = cosθ3/p3
cosθ1>cosθ2>cosθ3as p1>p2>p3
0≤θ1<θ2<θ3 <Π/2
A rectangular film of liquid is extended from (4 cm × 2cm) to (5 cm × 4 cm). If the work done is 3 × 10–4 J, the value of the surface tension of the liquid is
Increase in surface area = (20 cm2-8 cm2)×2
= 12×2 cm2
= 24 cm2 (film has two surfaces)
So work done = T Δ S = T × 24 × 10-4 = 3×10-4
so T = 3/24 N/m = 1/8 Nm-1 = 0.125 N/m
A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is
TE = GMm/2(R+h) = -GMm/2(R+h) R2/R2 = g0mR2/2(R+h)
Starting from the centre of the earth having radius r, the variation of g (acceleration due to gravity) is shown by
A light rod of length l has two masses m1 and mattached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is :
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Esphere / E cylinder) will be :
Two rotating bodies A and B of masses m and 2m with moments of inertia IA and IB (IB > IA) have equal kinetic energy of rotation. If LA and LB be their angular momenta respectively, then
Two identical balls A and B having velocities of 0.5 m/s and –0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be
Mass of balls are same and the collision is perfectly elastic, so their velocity will be interchanged.
So, VA = – 0.3 m/s, VB = 0.5 m/s
A bullet of mass 10 g moving horizontally with a velocity of 400 ms–1 strikes of wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be
During the collision, apply moementum conservation (0.01)(400) + 0 = (2)V + (0.01)V'
where V = √2gh
V = √2 ×10× 0.1
V = √2 solving
V' = 120 m/sec. Ans.
A rigid ball of mass m strikes a rigid wall at 60º and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall in the ball will be
J = 2mV cos 60 = mV
In the given figure, a = 15 m/s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is
Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xp(t) = at + bt2 and xQ (t) = ft – t2 . At what time do the cars have the same velocity
Vp=VQ
a + 2bt = f – 2t = t = f-a/2(b+1)
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has dimension of length?
What is the output Y in the following circuit, when all the three inputs A, B, C are first 0 and then 1 ?
The given circuit has two ideal diodes connected as shown in the figure below. The current flowing through the resistance R1 will be :
The diode D1 will be be in reverse bias, so it will block the current and diode D1 will be in forward bias, so it will pass the current
i = 10/ 2+2 = 2.5 A
For CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 4V. If the current amplification factor of the transistor is 100 and the base resistance is 1 kΩ, then the input signal voltage is :
The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is :
If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength λ. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be :
Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is :
Electrons of mass m with de-Broglie wavelength λ fall on the target in an X-ray tube. The cutoff wavelength (λ0) of the emitted X-ray is :
A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 × 10–5 cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is :