35 + Interview Questions in PHYSICAL-WORLD-AND-MEASUREMENTS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	The initial and final temperature of water were recorded as `(56.3 pm 0.4) ^(@)C` and `(27.5 + 0.3) ^(@)C` . Determine the fall in the temperature of water .
Answer» Correct Answer - `(28.8 pm 0.7) ^(@)C`

Discussion

2.	The length and breadth of a rectangular block are 25.2 cm and 16.8 cm, which have both been measurd to an accurancy of 0.1 cm find the area of the rectangular block.
Answer» Correct Answer - `1.0 %`

Discussion

3.	The length of two rods are recorded as `l_(1) = (25.2 pm 0.1)` cm and `l_(2) = (16.8 pm 0.1)` cm . Find their combined length .
Answer» Correct Answer - `(42.0 pm 0.2)` cm

Discussion

4.	Calculate the percentage error in specific resistance , `rho = pi r^(2) R // l `, where r = radius of wire `= 0.26 +- 0.02 cm` , l = length of wire `= 156.0 +- 0.1 cm`, and R = resistance of wire `= 64 +- 2 Omega`.
Answer» Correct Answer - `18.5 %`

Discussion

5.	In an experiment to measure focal length of a concave mirror , the value of focal length in successive observations turns out to be `17.3` cm , 17.8 cm , 18.3 cm , 18.2 cm , 17.9 cm and `18.0` cm . Calculate the mean absolute error and percentage error . Express the result in a proper way .
Answer» Correct Answer - `0.25` cm , `1.4% , (17.9 pm 0.25)` cm

Discussion

6.	The measured mass and volume of a body are `2.00` g and `5.0 cm^(3)` respectively . With possible errors of `0.01` g and `0.1 cm^(3)` , what would be the percent error in density ?
Answer» Correct Answer - `2.5 %`

Discussion

7.	The refractive index of water as measured by the relation `mu = ("Real depth")/("Apparent depth")` was found to have the values `1.29 , 1.33 , 1.34 , 1.35 , 1.32 , 1.36 , 1.30 , 1.33`. Calculate (i) mean value of `mu` (ii) mean value of absolute error (iii) relative error (iv) percentage error .
Answer» Correct Answer - (i) 1.32 , (ii) `0.02` (iii) `0.015` (iv) `1.5%`

Discussion

8.	A neutron star has a density equal to that of nuclear matter `(~= 2.8X0^(17) kg m^-3).` Assuming the star to be spherical, find the radius of the neutron star whose mass is `4.0X10^(30)kg.`
Answer» Correct Answer - 15 km

Discussion

9.	The diameter of a sphere is `2.78` m . Calculate its volume with due regard to significant figures .
Answer» Correct Answer - `11.25 m^(3)`

Discussion

10.	The diameter of a circle is 2.486 m. Calculate the area with due regard to significant figures.
Answer» Correct Answer - `4.854 m^(2)`

Discussion

11.	The diameter of a sphere is `4.24` m . Calculate its surface area with due regard to significant figures .
Answer» Correct Answer - `56.5 m^(2)`

Discussion

12.	State the number of significant figures in the following measurements : (i) `0.009 m^(2) " " (ii) 5.049 N m^(-2) " " (iii) 0.1890 g cm^(-3) " " (iv) 1.90 xx 10^(11) kg " " (v) 0.020800 m " " (vi) 5.308 J `
Answer» Correct Answer - (i) 1 (ii) 4 (iii) 4 (iv) 3 (v)5 (vi) 4

Discussion

13.	A 35 mm wide slide with 24 mm`xx` 36 mm picture is projected ona screen placed 12 cm from the slide. The image of the slide picture on the screen measures `1.0 m xx 1.5m`. What is the linear magnification of the arrangement ?
Answer» Correct Answer - 41.67

Discussion

14.	The parallex of a heavenly body measured ffrom two points diametrically opposite on equater of earth is 1.0 minutes. If the radius of the earth is 6400 m, find the distance of the heavenly body from the centre of the earth in AU. Given `1 AU=1.5xx10^(11)`m.
Answer» Correct Answer - 0.293 AU

Discussion

15.	In a submarine fitted with a SONAR, the time between the genretaion of an ultrasonicwave and the reciept of its echo is 200 s. What is the dsistance of the enemy sun=bmrine ? The speed of the sound in water is `1.450 km s^(-1)`
Answer» Correct Answer - 145 km

Discussion

16.	A rock under water is 1595 m deep. Find the time in which an ultrasonic signal returns after reflection from the rock. Speed of ultrasonic waves in water = `1450m//s`.
Answer» Correct Answer - 2.2 s

Discussion

17.	Find the distance of the moon from the earth if the parralrtic angle as measured from two places locaterd `6.4xx10^(6)`m apart is `1^(@)`.
Answer» Correct Answer - `3.67xx10^(8)`m

Discussion

18.	The angle of elevation of the top of a hill is `30^(@)` from a point on the ground. On walking 1 km towards the hill, angle is found to be `45^(@)`. Calculate the height of the hill.
Answer» Correct Answer - 1.366 km

Discussion

19.	Suppose the acceleration due to gravity at a place is `10 m/s^2`. Find its value in cm / `(minute)^2`.
Answer» Correct Answer - `3.6xx10^(6)cm min^(-2)`

Discussion

20.	The value of acceleration due to gravity at a place is `9.8ms^(-2)`. Find its value in `km h^(-2)`
Answer» Correct Answer - `127008kmh^(-2)`

Discussion

21.	A small spherical ball of radius r falls with velocity `upsilon` through a liquid having coeffiecinet of viscosity `eta.` find viscous darg F on the wall if it depends or `r, upsilon, eta. Take K = 6 pi`
Answer» Correct Answer - `F = 6 pi eta r v`

Discussion

22.	A student conclude that the velocity v of a body falling freely under gravity from a height is equal to `sqrt(gh)`. Using the method of dimensions, verify whether his coclusion is correct.
Answer» Correct Answer - Correct

Discussion

23.	The orbital velocity v of a satellite may depend on its mass m , the distane r from the centre of the earth and acceleration due to gravity g . Obtain an expression for its orbital velocity .
Answer» Correct Answer - `v = ksqrt(rg)`

Discussion

24.	What is one astronomical unit ? Express it in metres . Write its order og magnitude .
Answer» Correct Answer - (Order of magnitude =11)

Discussion

25.	Using the method of dimensions , derive an expressions for the energy of a body executing SHM , assuming this energy depends upon its mass m , frequency v and amplitude of vibration r .
Answer» Correct Answer - `E = Km v^(2) r^(2)`

Discussion

26.	The time period of a compound pendulum is given by `T=2pisqrt((I)/(mgl))` `{:(,"where","I=moment of inertia about the centre of the suspension,"),(,,"g=acceleration due to gravity , m=mass of the pendulam"),(,,"l=distance of the centre of the gravity from the centre of the suspension."):}`
Answer» Correct Answer - Correct

Discussion

27.	Write the order of magnitude of the following : (i) 8 (ii) 49 (iii)52 (iv) 999 (v) 1001 (vi) 753000 (vii) 0.05 (viii) 0.99
Answer» Correct Answer - (1,1,2,3,3,-2,0)

Discussion

28.	Obtain dimensions of (i) impulse (ii) power (iii) surface energy (iv) cofficent of viscecity (v) bulk modules (vi) force constant.
Answer» Correct Answer - (i) `MLT^(-1)` (ii) `ML^(2)T^(-3)` (iii) `ML^(0)T^(-2)` (iv) `ML^(-1)T^(-1)` (v) `ML^(-1)T^(-2)` (vi) `ML^(0)T^(-2)`

Discussion

29.	Calculate the dimensions of ther force and impulse taking velocity, density and frequency as basic quantities.
Answer» Correct Answer - `pv^(4)v^(-2),pv^(4)v^(-3)`

Discussion

30.	Deduce dimensional formulae for (i) angle (ii) angular velocity (iii) angular acceleration (iv) torque (v) angukar momentum and (vi) moment of inertia.
Answer» Correct Answer - (i) Dimensionless (ii) `T^(-1)` (iiI) `T^(-2)` (iv)`ML^(2)T^(-2)` (v) `ML^(2)T^(-1)` (vi) `ML^(2)`

Discussion

31.	If force (F), length(L) and time (T) as chosen as the fundamental quantities, then what would be the dimensional formula for the density?
Answer» Correct Answer - `FL^(-4)T^(-2)`

Discussion

32.	Solve the following to the appropriate number of significant figures : (i) `0.58 + 324.65` (ii) `3.124 xx 4.576 ` (iii) `(324 xx 0.08666)/(5.006)` `(1.35 xx 10^(-6) xx 0.4 )/(5.6)` (v) `(2.03 xx 10^(-5) xx 3.5 xx 10^(-7))/(0.6423)` (vi) `sqrt(3.5 - 3.31)`
Answer» Correct Answer - `325 . 23 ` `14.30` `0.0560` `0.0964 xx 10^(-4)` `(11.1 xx 10^(2))` `0.4`

Discussion

33.	Two atomic clocks allowend to run for a average life of an indian (say 70 years) differ by 0.2 s only. Calculate the accuracy of standard atomic clock in measuring a time interval of 1 sec.
Answer» Correct Answer - 1 sin `10^(10)` s

Discussion

34.	The cirtical angular velocity `omega_c` of a cylinder inside another cylinder containing a liquied at which its turbulance occurs depends on visocisity `eta` density `rho` and disntac d between wall of the cylinder. Obtain an expression for `omega_c` using method of dimensios.
Answer» Correct Answer - `omega_(c) = ( K eta)/(rho d^(2))`

Discussion

35.	Check the correctness of the equation : `y = a "sin" (omega t + phi)`, where y = displacement , a = amplitude , `omega` = angular frequency and `phi` is an angle .
Answer» Correct Answer - correct

Discussion

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The initial and final temperature of water were recorded as `(56.3 pm 0.4) ^(@)C` and `(27.5 + 0.3) ^(@)C` . Determine the fall in the temperature of water .

The length and breadth of a rectangular block are 25.2 cm and 16.8 cm, which have both been measurd to an accurancy of 0.1 cm find the area of the rectangular block.

The length of two rods are recorded as `l_(1) = (25.2 pm 0.1)` cm and `l_(2) = (16.8 pm 0.1)` cm . Find their combined length .

Calculate the percentage error in specific resistance , `rho = pi r^(2) R // l `, where r = radius of wire `= 0.26 +- 0.02 cm` , l = length of wire `= 156.0 +- 0.1 cm`, and R = resistance of wire `= 64 +- 2 Omega`.

In an experiment to measure focal length of a concave mirror , the value of focal length in successive observations turns out to be `17.3` cm , 17.8 cm , 18.3 cm , 18.2 cm , 17.9 cm and `18.0` cm . Calculate the mean absolute error and percentage error . Express the result in a proper way .

The measured mass and volume of a body are `2.00` g and `5.0 cm^(3)` respectively . With possible errors of `0.01` g and `0.1 cm^(3)` , what would be the percent error in density ?

The refractive index of water as measured by the relation `mu = ("Real depth")/("Apparent depth")` was found to have the values `1.29 , 1.33 , 1.34 , 1.35 , 1.32 , 1.36 , 1.30 , 1.33`. Calculate (i) mean value of `mu` (ii) mean value of absolute error (iii) relative error (iv) percentage error .

A neutron star has a density equal to that of nuclear matter `(~= 2.8X0^(17) kg m^-3).` Assuming the star to be spherical, find the radius of the neutron star whose mass is `4.0X10^(30)kg.`

The diameter of a sphere is `2.78` m . Calculate its volume with due regard to significant figures .

The diameter of a circle is 2.486 m. Calculate the area with due regard to significant figures.

The diameter of a sphere is `4.24` m . Calculate its surface area with due regard to significant figures .

State the number of significant figures in the following measurements : (i) `0.009 m^(2) " " (ii) 5.049 N m^(-2) " " (iii) 0.1890 g cm^(-3) " " (iv) 1.90 xx 10^(11) kg " " (v) 0.020800 m " " (vi) 5.308 J `

A 35 mm wide slide with 24 mm`xx` 36 mm picture is projected ona screen placed 12 cm from the slide. The image of the slide picture on the screen measures `1.0 m xx 1.5m`. What is the linear magnification of the arrangement ?

The parallex of a heavenly body measured ffrom two points diametrically opposite on equater of earth is 1.0 minutes. If the radius of the earth is 6400 m, find the distance of the heavenly body from the centre of the earth in AU. Given `1 AU=1.5xx10^(11)`m.

In a submarine fitted with a SONAR, the time between the genretaion of an ultrasonicwave and the reciept of its echo is 200 s. What is the dsistance of the enemy sun=bmrine ? The speed of the sound in water is `1.450 km s^(-1)`

A rock under water is 1595 m deep. Find the time in which an ultrasonic signal returns after reflection from the rock. Speed of ultrasonic waves in water = `1450m//s`.

Find the distance of the moon from the earth if the parralrtic angle as measured from two places locaterd `6.4xx10^(6)`m apart is `1^(@)`.

The angle of elevation of the top of a hill is `30^(@)` from a point on the ground. On walking 1 km towards the hill, angle is found to be `45^(@)`. Calculate the height of the hill.

Suppose the acceleration due to gravity at a place is `10 m/s^2`. Find its value in cm / `(minute)^2`.

The value of acceleration due to gravity at a place is `9.8ms^(-2)`. Find its value in `km h^(-2)`

A small spherical ball of radius r falls with velocity `upsilon` through a liquid having coeffiecinet of viscosity `eta.` find viscous darg F on the wall if it depends or `r, upsilon, eta. Take K = 6 pi`

A student conclude that the velocity v of a body falling freely under gravity from a height is equal to `sqrt(gh)`. Using the method of dimensions, verify whether his coclusion is correct.

The orbital velocity v of a satellite may depend on its mass m , the distane r from the centre of the earth and acceleration due to gravity g . Obtain an expression for its orbital velocity .

What is one astronomical unit ? Express it in metres . Write its order og magnitude .

Using the method of dimensions , derive an expressions for the energy of a body executing SHM , assuming this energy depends upon its mass m , frequency v and amplitude of vibration r .

The time period of a compound pendulum is given by `T=2pisqrt((I)/(mgl))` `{:(,"where","I=moment of inertia about the centre of the suspension,"),(,,"g=acceleration due to gravity , m=mass of the pendulam"),(,,"l=distance of the centre of the gravity from the centre of the suspension."):}`

Write the order of magnitude of the following : (i) 8 (ii) 49 (iii)52 (iv) 999 (v) 1001 (vi) 753000 (vii) 0.05 (viii) 0.99

Obtain dimensions of (i) impulse (ii) power (iii) surface energy (iv) cofficent of viscecity (v) bulk modules (vi) force constant.

Calculate the dimensions of ther force and impulse taking velocity, density and frequency as basic quantities.

Deduce dimensional formulae for (i) angle (ii) angular velocity (iii) angular acceleration (iv) torque (v) angukar momentum and (vi) moment of inertia.

If force (F), length(L) and time (T) as chosen as the fundamental quantities, then what would be the dimensional formula for the density?

Solve the following to the appropriate number of significant figures : (i) `0.58 + 324.65` (ii) `3.124 xx 4.576 ` (iii) `(324 xx 0.08666)/(5.006)` `(1.35 xx 10^(-6) xx 0.4 )/(5.6)` (v) `(2.03 xx 10^(-5) xx 3.5 xx 10^(-7))/(0.6423)` (vi) `sqrt(3.5 - 3.31)`

Two atomic clocks allowend to run for a average life of an indian (say 70 years) differ by 0.2 s only. Calculate the accuracy of standard atomic clock in measuring a time interval of 1 sec.

The cirtical angular velocity `omega_c` of a cylinder inside another cylinder containing a liquied at which its turbulance occurs depends on visocisity `eta` density `rho` and disntac d between wall of the cylinder. Obtain an expression for `omega_c` using method of dimensios.

Check the correctness of the equation : `y = a "sin" (omega t + phi)`, where y = displacement , a = amplitude , `omega` = angular frequency and `phi` is an angle .