Advertisements
Advertisements
Question
The masses of two bodies are measured to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg. What is the total mass of the two and the error in it?
Advertisements
Solution
Given: A ± ΔA = 15.7 ± 0.2 kg and
B ± ΔB = 27.3 ± 0.3 kg.
To find: Total mass (Z), and total error (ΔZ).
Formulae:
i. Z = A + B
ii. ± ΔZ = ± ΔA ± ΔB
Calculation: From formula (i),
Z = 15.7 + 27.3 = 43 kg
From formula (ii),
± ΔZ = (± 0.2) + (± 0.3)
= ± (0.2 + 0.3)
= ± 0.5 kg
Total mass is 43 kg and total error is ± 0.5 kg.
APPEARS IN
RELATED QUESTIONS
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
Define absolute error.
Define Mean absolute error.
Define percentage error.
Answer the following question.
Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`
In a workshop, a worker measures the length of a steel plate with Vernier calipers having a least count 0.01 cm. Four such measurements of the length yielded the following values: 3.11 cm, 3.13 cm, 3.14 cm, 3.14 cm. Find the mean length, the mean absolute error, and the percentage error in the measured value of the length.
Find the percentage error in kinetic energy of a body having mass 60.0 ± 0.3 g moving with a velocity of 25.0 ± 0.1 cm/s.
Solve the numerical example.
If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density.
Solve the numerical example.
If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = `(A^2B^(1/2))/(C^(1/3)D^3)`, will be:
If Q = `"X"^"n"/"Y"^"m"` and Δx is absolute error in the measurement of X, Δy is absolute error in the measurement of Y, then absolute error ΔQ in Q is ______.
The relative density of a metal may be found by hanging a block of the metal from a spring balance and nothing that in air, the balance reads (5 .00 ± 0.05)N while in water, it reads (4.00 ± 0.05)N. The relative density would be quoted as ______.
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.
The resistance R = `"V"/"I"`, where V = (50 ± 2) V and I = (20 ± 0.2)A. The percentage error in R is 'x' %.
The value of x to the nearest integer is ______.
In a Screw Gauge, the fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation, the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with the reference line. Calculate the true reading.
If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M−5G−2 are ______.
The dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.
A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ × 10-6 m.
The least count of the main scale of a screw gauge is 1 mm. The minimun number of divisions on its circular scale required to measure 5 µm diameter of a wire is ______.
Reading a graduated cylinder at an angle (parallax error) is a specific example of which type of systematic error?
Systematic errors cause all measurements to shift in the same direction. What does this primarily affect?
What are random errors?
Which of the following is an environmental error?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Constant error can be caused due to ______.
