Balbharati solutions for Physics [English] 11 Standard Maharashtra State Board chapter 1 - Units and Measurements [Latest edition]

[L¹M¹T^-2] is the dimensional formula for ______.

The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.

Choose the correct option.

A light year is a unit of ______.

Dimensions of kinetic energy are the same as that of ______.

Choose the correct option.

Which of the following is not a fundamental unit?

Answer the following question.

Star A is farther than star B. Which star will have a large parallax angle?

Answer the following question.

What are the dimensions of the quantity `lsqrt(l//g)`, l being the length, and g the acceleration due to gravity?

Define absolute error.

Define Mean absolute error.

Define relative error.

Define percentage error.

Answer the following question.

Describe what is meant by significant figures.

Answer the following question.

Describe what is meant by order of magnitude.

If the measured values of the two quantities are A ± ΔA and B ± ΔB, ΔA and ΔB being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = `"A"/"B"`

`(Delta "Z")/"Z" = (Delta "A")/"A" + (Delta "B")/"B"`

Answer the following question.

Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`

Derive the formula of the kinetic energy of a particle having mass ‘m’ and velocity ‘v’, using dimensional analysis.

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?

The distance travelled by an object in time (100 ± 1)s is (5.2 ± 0.1) m. What are the speed and its maximum relative error?

An electron with charge e enters a uniform magnetic field `vec"B"` with a velocity `vec"v"`. The velocity is perpendicular to the magnetic field. The force on the charge is given by `|vec"F"|`= B e v. 
Obtain the dimensions of `vec"B"`.

Solve the numerical example.

A large ball 2 m in radius is made up of a rope of square cross-section with edge length 4 mm. Neglecting the air gaps in the ball, what is the total length of the rope to the nearest order of magnitude?

Solve the numerical example.

Nuclear radius R has a dependence on the mass number (A) as R =1.3 × 10^-16 A^1/3 m. For a nucleus of mass number A = 125, obtain the order of magnitude of R expressed in the meter.

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.

In Ohm’s experiments, the values of the unknown resistances were found to be 6.12 Ω, 6.09 Ω, 6.22 Ω, 6.15 Ω. Calculate the (mean) absolute error, relative error, and percentage error in these measurements.

An object is falling freely under gravitational force. Its velocity after travelling a distance h is v. If v depends upon gravitational acceleration g and distance, prove with the dimensional analysis that v = k`sqrt"gh"` where k is a constant.

v = `at + b/(t + c) + "v"_0` is a dimensionally valid equation. Obtain the dimensional formula for a, b and c where v is velocity, t is time and v₀ is initial velocity.

The length, breadth, and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

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.

When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72'' of arc. Calculate the diameter of Jupiter.

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.

Solve the numerical example.

Write down the number of significant figures in the following: 0.003 m², 0.1250 gm cm^-2, 6.4 x 10⁶ m, 1.6 x 10^-19 C, 9.1 x 10^-31 kg.

Solve the numerical example.

The diameter of a sphere is 2.14 cm. Calculate the volume of the sphere to the correct number of significant figures.