Which of the following pair have same dimension?
(a) L/R and CR (b) LR and CR
(c) R/L and [LC]1/2 (d) CR and 1/LC
The dimensions of physical quantities are represented by different units, such as length (L), time (T), mass (M), etc. In order for two quantities to have the same dimension, they must have the same combination of these fundamental units.
Let’s analyze each option:
(a) L/R and CR: L/R represents the unit of inductance divided by resistance, while CR represents the unit of capacitance times resistance. These two quantities have different dimensions, so they do not have the same dimension.
(b) LR and CR: LR represents the unit of inductance times resistance, while CR represents the unit of capacitance times resistance. These two quantities have the same dimension, as both involve the combination of resistance and inductance. Therefore, option (b) is correct.
(c) R/L and [LC]1/2: R/L represents the unit of resistance divided by inductance, while [LC]1/2 represents the square root of the product of capacitance and inductance. These two quantities have different dimensions, so they do not have the same dimension.
(d) CR and 1/LC: CR represents the unit of capacitance times resistance, while 1/LC represents the inverse of the product of capacitance and inductance. These two quantities have different dimensions, so they do not have the same dimension.
Therefore, the correct answer is (b) LR and CR.
- A bullet fired into a fixed target loses half of its velocity after penetrating
3 cm, the further distance travelled before coming to the rest is
(a) 4 cm. (b) 2 cm. (c) 3 cm. (d) 1 cm.
- The horizontal range is 4√3 times the maximum height in a projectile
motion. The angle of projection is
. (b) 45o
. (c) 30o
. (d) 60o
To solve this problem, let’s assume that the angle of projection is θ, the maximum height reached is H, and the horizontal range is R.
The horizontal range, R, of a projectile is given by the formula:
R = (v^2 * sin(2θ)) / g
where v is the initial velocity of the projectile and g is the acceleration due to gravity.
The maximum height, H, reached by the projectile is given by the formula:
H = (v^2 * sin^2(θ)) / (2g)
Given that the horizontal range is 4√3 times the maximum height, we can write the equation:
R = 4√3 * H
Substituting the formulas for R and H, we have:
(v^2 * sin(2θ)) / g = 4√3 * [(v^2 * sin^2(θ)) / (2g)]
Simplifying the equation:
sin(2θ) = 2√3 * sin^2(θ)
Using the identity: sin(2θ) = 2sin(θ)cos(θ), we can rewrite the equation as:
2sin(θ)cos(θ) = 2√3 * sin^2(θ)
Dividing both sides by 2sin(θ), we get:
cos(θ) = √3 * sin(θ)
Dividing both sides by sin(θ), we get:
cot(θ) = √3
Using the table of trigonometric values, we find that the angle whose cotangent is √3 is 30°.
Therefore, the correct answer is (c) 30°.
- The ‘net force acting on a body is zero’ then the wrong statement is
(a) body is at rest. (b) acceleration is not zero.
(c) body is in motion. (d) Acceleration should be zero.
The correct answer is (d) Acceleration should be zero.
According to Newton’s second law of motion, the net force acting on a body is equal to the product of its mass and acceleration (F = ma). If the net force on a body is zero, it means that the forces acting on the body are balanced, and there is no acceleration.
Therefore, when the net force acting on a body is zero, the correct statement is that the body is either at rest (option a) or in motion with constant velocity (since acceleration is zero). Option (c) is incorrect because it implies that the body is in motion with changing velocity, which would require a non-zero net force.
- If length of wire is doubled keeping the diameter constant, it’s Young’s
(a) increases. (b) decreases.
(c) remain same. (d) depend upon nature of matter.
The correct answer is (c) remain the same.
Young’s modulus is a measure of the stiffness or elasticity of a material and is defined as the ratio of stress to strain within the elastic limit of the material. It is a property of the material itself and is independent of the dimensions of the sample.
When the length of a wire is doubled while keeping the diameter constant, the cross-sectional area of the wire remains the same. As Young’s modulus is determined by the material’s intrinsic properties and not its dimensions, doubling the length of the wire does not affect its Young’s modulus.
Therefore, the Young’s modulus will remain the same in this case.
- The work done to blow a soap bubble of radius ‘R’ is W, then work done
to increase the radius from R to 3R is
(a)2 W. (b) 8 W. (c) 4 W. (d) 9 W.
The correct answer is (b) 8 W.
The work done to blow a soap bubble of radius R can be expressed as the change in surface energy of the bubble. Let’s assume the surface tension of the soap solution is represented by the symbol ‘S’.
The surface area of a sphere is given by A = 4πR^2. So, the initial surface energy of the bubble is E = 4πR^2S.
To increase the radius from R to 3R, the final surface area of the bubble will be A’ = 4π(3R)^2 = 36πR^2.
The change in surface energy ΔE is given by ΔE = E’ – E, where E’ is the final surface energy.
ΔE = 36πR^2S – 4πR^2S = 32πR^2S
The work done to increase the radius from R to 3R is equal to the change in surface energy, so the work done is W = 32πR^2S.
Now, if we substitute R with 3R, we get:
W’ = 32π(3R)^2S = 288πR^2S
Comparing this with the initial work done W, we can see that W’ is 8 times the initial work W. Therefore, the work done to increase the radius from R to 3R is 8 times the initial work, which is 8W.
Hence, the correct answer is (b) 8 W.
- A metallic ball is immersed in alcohol. The coefficient of cubical
expansion of metal is less than that of alcohol. When the system is
heated weight of ball is
(a) increases. (b) remains unchanged
(c) decreases. (d) First increases and then
The correct answer is (c) decreases.
When a metallic ball is immersed in alcohol and the system is heated, both the metal ball and the alcohol expand due to the increase in temperature. However, since the coefficient of cubical expansion of the metal is less than that of alcohol, the metal ball will expand less compared to the alcohol.
As the metal ball expands less than the alcohol, its volume increases at a slower rate. According to Archimedes’ principle, the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Since the volume of the metal ball increases at a slower rate than the alcohol, the increase in buoyant force experienced by the metal ball will be less compared to the alcohol.
As a result, the weight of the metal ball will decrease when the system is heated. This is because the decrease in the effective weight of the ball due to the reduced buoyant force outweighs the increase in weight caused by the expansion of the ball itself.
Therefore, the correct answer is (c) decreases
- Latent heat of a substance is zero at
(a) boiling point. (b) critical temperature.
(c) melting point. (d) freezing point.
The correct answer is (c) melting point.
The latent heat of a substance refers to the amount of heat energy required or released during a phase change without a change in temperature. It is the heat energy associated with the transformation of a substance from one phase to another (e.g., solid to liquid or liquid to gas) at a constant temperature.
At the melting point, a substance transitions from a solid phase to a liquid phase. During this phase change, the substance absorbs heat energy from its surroundings without a change in temperature. This heat energy is used to overcome the intermolecular forces holding the particles together in the solid phase, allowing them to move more freely in the liquid phase.
The latent heat of fusion, which is the heat energy absorbed during the melting process, is not zero at the melting point. It is the heat energy required to convert a substance from a solid to a liquid phase at its melting point.
Therefore, the correct answer is (c) melting point.
- The average Kinetic Energy per degree of freedom per molecule of an
ideal gas is
(a) KT. (b) 2KT. (c) ½ KT. (d) ¾ KT.
B.Sc. CSIT Entrance Examination Model Question 3
- Two spheres of same material have radii in the ration 3:2. The heat
radiated by them at the same temperature will be
(a) 1:1. (b) 4:9. (c) 9:4. (d) 3:2.
- Light of wavelength 550 nm falls normally on a slit of width 22 × 10-7m,
the angular position of second minima from central maxima will be
. (c) 420
. (d) 620
- A person is in a room whose ceiling and two adjacent walls are mirrors.
Number of images formed of an object is
(a) 5. (b) 7. (c) 6. (d) 8.
- The refractive index is 1.414 and refracting angle is 60o
, then minimum
deviation of light will be
. (b) 60o
. (c) 45o
. (d) 72o
- A sound wave has frequency 500 Hz and velocity 360 m/s. What is the
distance between 2 particles having phase difference 600
(a) 0.7 cm (b) 70 cm (c) 1.2 cm (d) 12 cm
- Two fixed charges q and 4q are at r distance apart. What will be position
of third charge to be placed so that the system will be in equilibrium?
(a)2r/3 from 4q (b )2r from q (c) r/2 from q (d) r/2 from 4q
- n-equal capacitors are first connected in series and then in parallel. The
ratio of maximum to minimum capacitance is
. (b) 1/n2
. (c)n. (d) 1/n.
- A heater coil is cut into two equal parts and only one part is used in the
heater. How will the heat generated vary?
(a) One fourth (b) Doubled (c) Halved (d) Four times
- A 50 V battery is connected across 10 Ohm resistor. The current in the
circuit is 4.5 Ampere. The internal resistance of the battery should be
(a) zero (b) 5.0 Ohm (c) 0.5 Ohm (d) 1.1 Ohm
- A magnetic needle kept in a non-uniform magnetic field. It experiences
(a) a torque but not a force (b)a force and a torque
(c) neither a force nor a torque (d) a force but not a torque
- In LCR circuit, the inductive reactance at resonance frequency is 100 Hz
and resistance is 5 Ohm, the quality factor of the circuit is
(a) 5000. (b)500. (c) 20. (d) 95.
- A circuit contains a capacitor of 420 Pf and an inductance L. The value
of ‘L’ to broadcast on Radio at 1020 kHz is
(a) 2.8 x 10-5 H. (b) 7.6 x 10-5 H. (c) 5.8 x 10-5 H. (d) 9.6 x 10-6 H.
- Electron accelerated from rest to a potential difference of 100 volt, its
final velocity will be
(a) 5 x 105 m/s. (b) 3 x 106 m/s. (c) 4 x 105 m/s. (d) 6 x 106 m/s.
- When a proton collides with an electron, which of the following
characteristics of proton increases?
(a) Energy (b) Wavelength (c) Frequency (d) Impulse
- The half life of a radioactive sample is 10 years. Its mean life is
(a) 12.43 years. (b) 16.43 years.
(c) 14.43 years. (d) Same as half life.
- NPN transistors are most preferred than that of PNP transistor. It is
(a) low cost. (b) capable of handling low power.
(c) Low dissipation of energy. (d)high mobility of electrons than holes.