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All questions of Measurement and Units for JAMB Exam

A particle is moving along a circle of radius R such that it completes one revolution in 40 seconds. What will be the displacement after 2 minutes 20 seconds?
  • a)
    6R
  • b)
    2R
  • c)
    4R
  • d)
    R
Correct answer is option 'B'. Can you explain this answer?

Nandini Patel answered
1 revolution in 40 seconds
In 1 second it covers = 1/40 revolution
In 140 sec = 1/40 * 140 =7/2 rotation = 3 and half rotation
Then the particle will be on the diametrically opposite end. 
Therefore, Displacement = R + R = 2R

Which of the following physical quantity has different dimension than others?
  • a)
    Energy
  • b)
    Watt hour
  • c)
    Momentum
  • d)
    Work
Correct answer is option 'C'. Can you explain this answer?

Riya Banerjee answered
Dimension of work and energy are the same i.e. [ML²T⁻²].
 Power = Energy/Time,
 Energy = Power × Time (in terms of hour instead of second),
 Energy = Watt × Hour,
= [ML²T⁻³] [T],
= [ML²T⁻²].
But, Momentum(p) = Mass × Velocity,
 p = [M] [LT⁻¹],
 p = [MLT⁻¹].
Hence the Dimension of work, energy and watt-hour is the same i.e. [ML²T⁻²] but the dimension of momentum is different ([MLT⁻¹]).

The ratio of magnitude of velocity and speed is always:
  • a)
    Equal to or less than one
  • b)
    Less than one
  • c)
    One
  • d)
    Equal to or greater than one
Correct answer is option 'A'. Can you explain this answer?

Anjana Sharma answered
The displacement of the body in given time is always equal to or less than distance covered, because, velocity is displacement per unit time and speed is distance covered per unit time, therefore, ratio of magnitude of velocity and speed is always equal to or less than one.

Which is the most accurate atomic clock?
  • a)
    Carbon-12 clock
  • b)
    Carbon atom clock
  • c)
    caesium atom clock
  • d)
    Stop clock
Correct answer is option 'C'. Can you explain this answer?

Nandini Patel answered
According to the most accurate caesium atomic clock in the world, 1 second is the time that elapses during 9,192,631,770 cycles of the radiation produced by the transition between two levels of the caesium 133 atom.

Can you explain the answer of this question below:
The method used to measure the distance of a planet from the earth is
  • A:
    Parallax method
  • B:
    Archimedes’ method
  • C:
    Newton’s method
  • D:
    Galileo’s method
The answer is a.

Yash Ghoshal answered
The astronomers mainly use parallax method to find distances to objects like other planets. To calculate the distance to a star or to a planet, astronomers observe it from different places along Earth's orbit around the Sun.

Which of the following is not an example of a rectilinear motion?
  • a)
    A car moving on a straight road.
  • b)
    A rain drop falling towards the earth.
  • c)
    A car moving in a circular path.
  • d)
    A wooden block sliding down the inclined plane.
Correct answer is option 'A'. Can you explain this answer?

Neha Joshi answered
Rectilinear motion is another name for straight-line motion
A body is said to experience rectilinear motion if any two particles of the body travel the same distance along two parallel straight lines.
A car moving in a circular path changes its direction at every instant. Thus, it is not the rectilinear motion.

A vehicle travels half the distance L with speed V1and the other half with speed V2, then its average speed is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Gaurav Kumar answered

 
Let the vehicle travels from A to B. Distances, velocities, and time taken are shown. To calculate average speed we will calculate the total distance covered and will divide it by the time interval in which it covers that total distance. 
Time taken to travel first half distance t1
Time taken to travel first half distance t1
Total time taken = t+ t2
We know that vav ​= Average speed = Total Distance / Total Time
 

 The numerical ratio of velocity to speed is:
  • a)
    Either less than or equal to 1
  • b)
    Equal to 1
  • c)
    Greater than 1
  • d)
    Less than 1
Correct answer is option 'A'. Can you explain this answer?

Charvi Mehta answered
When an object is moving along a straight path, magnitude of average velocity is equal to the average speed. Therefore, numerical ratio of average velocity to average speed is one in a straight line motion.
But, during curved motion, the displacement<distance covered, so the velocity<speed.

The number of significant digits in 8.1000 is
  • a)
    3
  • b)
    1
  • c)
    5
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?

Krishna Iyer answered
There are three rules on determining how many significant figures are in a number: 
  • Non-zero digits are always significant.
  • Any zeros between two significant digits are significant.
  • A final zero or trailing zeros in the decimal portion ONLY are significant.
Keeping these rules in mind, we can say that there are 5 significant digits.

Can you explain the answer of this question below:

 Which of the following is caused by careless handling?

  • A:

    Systematic error

  • B:

    Gross error

  • C:

    Random error

  • D:

    None of the mentioned

The answer is b.

Nandini Iyer answered
Gross errors are mostly due to lack of knowledge, judgment and care on the part of experiment. That is Gross error is caused by careless handling.

The ratio of displacement to distance is
  • a)
    Greater than 1
  • b)
    Either less than or equal to 1
  • c)
    Less than 1
  • d)
    Equal to 1
Correct answer is option 'B'. Can you explain this answer?

Saumya Dey answered
Ratio of Displacement to Distance

Displacement and distance are two terms used in physics to describe the motion of an object. Displacement refers to the change in position of an object from its initial to final position, whereas distance refers to the total path covered by the object during its motion.

Ratio of Displacement to Distance Formula

The ratio of displacement to distance is given by:

Displacement / Distance

This ratio is used to determine the efficiency of an object's motion. If the ratio is equal to 1, it means that the object has moved in a straight line from its initial to final position. If the ratio is less than 1, it means that the object has taken a longer path to reach its final position, and if the ratio is greater than 1, it means that the object has moved back and forth before reaching its final position.

Answer Explanation

The correct answer to the question is option B, which states that the ratio of displacement to distance is either less than or equal to 1. This is because an object can never cover a greater distance than its displacement. The displacement represents the shortest distance between the initial and final positions of an object, whereas the distance represents the total path covered by the object.

Therefore, the displacement can be equal to or less than the distance covered by the object, but it can never be greater than the distance. This is the reason why the ratio of displacement to distance is either less than or equal to 1.

The number of significant digits in 48,923 is
  • a)
    2
  • b)
    4
  • c)
    3
  • d)
    5
Correct answer is option 'D'. Can you explain this answer?

Rohit Joshi answered
There are three rules on determining how many significant figures are in a number: Non-zero digits are always significant.Any zeros between two significant digits are significant.A final zero or trailing zeros in the decimal portion ONLY are significant.Keeping these rules in mind, we can say that there are 5 significant digits.

The number of significant digits in 0.007 is
  • a)
    4
  • b)
    3
  • c)
    2
  • d)
    1
Correct answer is option 'D'. Can you explain this answer?

Om Desai answered
There are three rules on determining how many significant figures are in a number:
  • Non-zero digits are always significant.
  • Any zeros between two significant digits are significant.
  • A final zero or trailing zeros in the decimal portion ONLY are significant.
So, keeping these rules in mind, there are 1 significant digit.

 The numbers of significant figures in 1.84 x10-27 kg are:
  • a)
    five
  • b)
    thirty
  • c)
    three
  • d)
    four
Correct answer is option 'C'. Can you explain this answer?

Suresh Iyer answered
As the given number is itself written in the format of powers of ten, it is very obvious that all the non significant zeros are considered by the power of the and hence all the rest digits that are 3 in number are significant.

A dimensionless quantity
  • a)
    has no unit
  • b)
    must have a unit
  • c)
    cannot exist
  • d)
    might have a unit
Correct answer is option 'D'. Can you explain this answer?

Rajeev Saxena answered
A unit need not always mean a physical unit. So a dimensionless quantity will always be independent of the base units — meter, second, kilograms, kelvin, candela, moles, ampere.
But there are other quantities that are dimensionless, but have a unit. For example, radian is the unit for an angle. But it is dimensionless because it is defined to be the ratio of two lengths.

 Which of the following is caused by careless handling?
  • a)
    Systematic error
  • b)
    Gross error
  • c)
    Random error
  • d)
    None of the mentioned
Correct answer is option 'B'. Can you explain this answer?

Gross errors are mostly due to lack of knowledge, judgment and care on the part of experiment. That is Gross error is caused by careless handling.

Dimensions cannot be used to
  • a)
    check dimensional correctness of a formula
  • b)
    convert units
  • c)
    find value of the constant of proportionality in an equation
  • d)
    deduce a relation among physical quantities
Correct answer is option 'C'. Can you explain this answer?

Preeti Iyer answered
  • Dimensional Equations are used to derive the Relations between the Physical quantities . Also, they are used to check the correctness of the Equation by the Principle of the homogeneity of the dimensions. Hence, Option (a) and option (b) are true for the Dimensional equation. Thus, It is not correct for the given questions.
  • Dimensional Equations are not valid for the Pure numbers since they are non-dimensional constants.and also they do not provide the Value of the Constant of the Proportionality.
  • Thus, we can also say that all equations which are correct must be dimensionally correct but all those equations which are dimensionally correct may or may not be accurately correct. Thus, Option Option (c). is correct answer for the Given question.
  • Dimensional Equations are used for the conversions of the units thus this option can not be correct for the given question.

The product of energy and time is called action. The dimensional formula for action is same as that for
  • a)
     Power
  • b)
     Angular energy
  • c)
    Force × velocity
  • d)
     Impulse × distance
Correct answer is option 'D'. Can you explain this answer?

Hansa Sharma answered
Both are different from each other.
Energy × Time=(M1L2T−2)×(T1)=M1L2T−1
Force × Velocity=(M1L1T−2)×(L1T−1)=M1L2T−3
Impulse × distance=(M1L1T−1)×(L1)=M1L2T−1
Power=M1L2T−3
Angular Energy=M1L1T−2

Find the option with 5 significant figures
  • a)
    26.08mm
  • b)
    0.02608m
  • c)
    2.608cm
  • d)
    2.6008 cm
Correct answer is option 'D'. Can you explain this answer?

Preeti Iyer answered
In option a, b and c, we only have 4 significant figures in the number
In option d, the number has 5 significant figures.

 Find the option with 3 significant figures.
  • a)
    0.0268
  • b)
    2.068
  • c)
    2.608
  • d)
    26.08
Correct answer is option 'A'. Can you explain this answer?

Raghav Bansal answered
0.0268 have three significant figures where as 2.608 cm, 26.08 mm and 2.068 cm have four significant figures.

The significant digits in 0.000532 are:
  • a)
    2, 3
  • b)
    5, 3, 2
  • c)
    0,5,3,2
  • d)
    5, 3
Correct answer is option 'B'. Can you explain this answer?

Rishu Singh answered
Option B is correct
5, 3 and 2 are significant figures in 0.000532
zero before furst non zero digit from left are always
INSIGNIFICANT

If a and b are two physical quantities having different dimensions then which of the following can denote a new physical quantity
  • a)
    a + b
  • b)
    a – b
  • c)
    a/b
  • d)
    ea/b
Correct answer is option 'C'. Can you explain this answer?

Suresh Reddy answered
Quantities with different dimensions cant be added or subtracted. Also the dimension of the product of the quantities in power is always one. But when two quantities are multiplied the dimension of the product is the product of the dimensions of the initial quantities.

The number of significant digits in 2,076 is
  • a)
    3
  • b)
    5
  • c)
    2
  • d)
    4
Correct answer is option 'D'. Can you explain this answer?

Preeti Iyer answered
There are three rules for determining how many significant figures are in a number: 
  • Non-zero digits are always significant.
  • Any zeros between two significant digits are significant.
  • A final zero or trailing zeros in the decimal portion ONLY are significant.
Keeping these rules in mind, we can say that there are 4 significant digits.

Can you explain the answer of this question below:

The physical quantities not having same dimensions are [AIEEE 2003]

  • A:

    Torque and work

  • B:

     Momentum and Planck's constant

  • C:

    Stress and Young's modulus

  • D:

     Speed and 

The answer is b.

Mira Sharma answered
Torque has same dimension as work, Stress has same dimensions as Young's modulus,Speed and (μ0∈0)^(−1/2) have same dimensionsbut Momentum and Plank's constant do not have same dimensionsHence b is the correct answer.

Can you explain the answer of this question below:

The numbers of significant figures in 9.1 x10-31 kg are:

  • A:

    three

  • B:

    two

  • C:

    ten

  • D:

    twenty one

The answer is b.

Om Desai answered
As the power of 10 is irrelevant to the determination of significant figures hence, the numbers of significant figures are 2 (9 and 1).

Which of the following is not the unit of energy?
  • a)
    watt-hour
  • b)
    electron-volt
  • c)
    N × m
  • d)
    kg × m/sec2
Correct answer is option 'D'. Can you explain this answer?

Rajat Patel answered
Newton • meter = F.d --> work 
foot-pound (symbol: ft.lb) is a unit of work or energy (Wiki) 
watt for power 
kilowatt hour, or kilowatt-hour, (symbol kWh, kW h or kWh) is a unit of energy (Wiki) 
joule for energy.

Population of a town is reported as 157,900 . Which of the following statements correct?
  • a)
    the population is 157900 20
  • b)
    the population is 157900 50
  • c)
    the population is 157900100
  • d)
    the population is 15790025
Correct answer is 'B'. Can you explain this answer?

Arun Khanna answered
Here, 157900 (the significant digits are underlined here) implies that the population is believed to be within the range of about 157850 to about 157950. In other words, the population is 157900�50. The “plus-or-minus 50” appended to this number means that we consider the absolute uncertainty of the population measurement to be 50 – (–50) = 100. We can also say that the relative uncertainty is 100/157900, which we can also express as 1 part in 1579, or 1/1579 = 0.000633, or about 0.06 percent.

Numbers of significant figures in the volume of a cube of side 6.103 m are:
  • a)
    2
  • b)
    4
  • c)
    3
  • d)
    1
Correct answer is option 'B'. Can you explain this answer?

Raghav Bansal answered
  • As per rule, zero between two non zero digits are significant.
  • The number of a significant figure in the length of the side is 4.
  • So the calculated volume should be rounded off to 4 significant figures. Multiplying numbers do not increase significant figures.

PARSEC is a unit of
  • a)
    Time
  • b)
    Angle
  • c)
    Distance
  • d)
    Velocity
Correct answer is option 'C'. Can you explain this answer?

Raghav Bansal answered
The parsec (symbol: pc) is a unit of length used to measure large distances to astronomical objects outside the Solar System. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to 648000π astronomical units.

Light year is the unit of
  • a)
    Speed
  • b)
    Mass
  • c)
    Distance
  • d)
    Time
Correct answer is option 'C'. Can you explain this answer?

Pooja Shah answered
The light-year is a unit of length used to express astronomical distances and measures about 9.46 trillion kilometres or 5.88 trillion miles. As defined by the International Astronomical Union, a light-year is the distance that light travels in vacuum in one Julian year. 

The respective number of significant figures for the numbers 23.023, 0.0003 and 21 × 10-3 are
  • a)
    5, 1, 2
  • b)
    5, 1, 5
  • c)
    5, 5, 2
  • d)
    4, 4, 2
Correct answer is 'A'. Can you explain this answer?

Rohan Singh answered
CORRECT OPTION IS (A).
(i) All the non-zero digits are significant. 

(ii) All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.

 (iii) If the number is less than 1, the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant. 

(iv) The power of 10 is irrelevant to the determination of significant figures. According to the above rules, 23.023 has 5 significant figures. 0.0003 has 1 significant figures. 2.1 X 10–3 has 2 significant figures.

A dimensionally consistent equation
  • a)
    is nearly correct
  • b)
    is always correct
  • c)
    is necessarily correct
  • d)
    is not necessarily correct
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
If an equation fails this consistency test, it is proved wrong, but if it passes, it is not proved right.
Thus, a dimensionally correct equation need not be actually an exact (correct) equation, but a dimensionally wrong (incorrect) or inconsistent equation is definitely wrong.

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