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Practice each question, then open the answer or worked solution.
Name the device used for measuring the mass of atoms and molecules.
Mass spectrograph is the device that is used for measuring the mass of atoms and molecules.
Short Answers(a) The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?
(b) Moon is seen to be of (½)° diameter from the earth. What must be the relative size compared to the earth?
(c) From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.
a)
The radius of the earth is treated as an arc as the distance between the moon and the earth is greater than the radius of the earth.
Let Re be the length of the arc
Distance between the moon and the earth = 60Re
Angle subtended by the diameter of the earth = 2o
b) The relative size of the moon, when compared to the earth, is = diameter of the earth/diameter of the moon = 4
c) The ratio of sun-earth diameter = Dsun/Dearth = 100
Which of the following time measuring devices is most precise?
Give the reason for your answer.
The correct option is d) an atomic clock as it measures up to one second.
The distance of a galaxy is of the order of 1025 m. Calculate the order of magnitude of time taken by light to reach us from the galaxy.
Distance of the galaxy = 1025m
Speed of light = 3 × 108 m/s
Time taken, t is
t = distance/speed = 3.33 × 1016 s
The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.
The minimum inaccuracy in the measurement of distance = (1/50)(0/5)mm = 0.01 mm
During a total solar eclipse-the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.
Rme is the distance of the moon from the earth
Rse is the distance of the sun from the moon
Asun is the area of the sun
Amoon is the area of the moon
Rs/Rm = Rse/Rme
If the unit of force is 100 N, unit of length is 10 m and unit of time is 100 s, what is the unit of mass in this system of units?
Force [F] = 100 N
Length [L] = 10 m
Time [t] = 100 s
2Substituting the values, we get M = 105 kg
Long AnswersA new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. How much will 5 J measure in this new system?
Let Q be the physical quantity = n1u1 = n2u2
Let M1, L1, T1 and M2,L2,T2 be the units of mass, length, and time for the given two systems.
n2 = n1
22M1 = 1 kg
L1 = 1 m
T1 = 1 s
M2 = α kg
L2 = β m
T1 = γ s
Substituting the values we get, n2 = 5γ2/αβ2 J
The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as
where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML–1T–1. Check whether the equation is dimensionally correct.
Dimension of the given physical quantity is
3-1-2LHS = [L3T-1]
RHS = [L3T-1]
LHS = RHS
Therefore, the equation is correct.
A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2 d–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.
The given physical quantity, X = a2 b3 c5/2 d–2
Percentage error in X = (∆x/x)(100)
Percentage error in a = (∆a/a)(100) = 1%
Percentage error in b = (∆b/b)(100) = 2%
Percentage error in c = (∆c/c)(100) = 3%
Percentage error in d = (∆d/d)(100) = 4%
Maximum percentage error in X = ±23.5%
X should have two significant values, therefore, X = 2.8