Previous Year Physics Question Papers (with solutions) of Kerala State Syllabus of Higher Secondary Examinations. Chapter Name: UNITS AND MEASUREMENTS

Mechanical power is represented by P = Fv + Av³ρ
where, F is the force, v is the velocity, A is the area and ρ is the density.
a) The dimensional formula of power is............
b) Check the dimensional validity of the above equation.
c) Which of the following equations can’t be obtained by the dimensional method?
i. T = 2π sqrt(l/g)
ii.E = kmv²
iii. P = hρg
iv. N = N₀ e^-λt

a) [ Power ] = M L² T^-3

b)
Apply Homogeneity Principle
[Fv] = MLT^-2LT^-1= M L² T^-3
[Av³ρ] = L² ( L T^-1 )³ M L^-3 = M L² T^-3
So the equation is correct

c) Option iv, since it involves expontial

a) A student was asked to write the equation for displacement at any instant in a simple harmonic motion of amplitude ‘a’. He wrote the equation as y = a sin (2πvt/k)
Where ‘v’ is the velocity at instant t sec. For the equation to be dimensionally correct, what should be the dimensions of k?
b) What is the area of a square of side 1.4 cm in proper significant figures?

a) Since angle is Dimensionless,
[vt] = [k]
[k] = LT^-1 T = L

b) 1.4 cm has 2 significant figures
Area = 1.96 cm ²
In proper significant figures Area should be rounded off to 2.0 cm²

Select the correct answer:
a) Light year is the unit of...........
i) time ii) length iii) year iv) velocity
b) kilowatt-hour is the unit of ......…
i) energy ii) power iii) time iv) mass

a) Light year is the unit of length
b) kilowatt-hour is the unit of energy

All physical quantities can be expressed in terms of dimension.
a) Write the physical quantities of the following dimensions:
i) [ M¹ L¹ T^-1] ii) [ M¹ L² T^-2]
b) Check whether the equation T = 2 π sqrt(L/T²)
Where T is Time period of a simple Pendulum, m is mass of the bob, L is the length of the Pendulum and g is acceleration due to gravity.

a)
i) Momentum or Impulse
ii) Work or Energy or Torque

b)
Use Homogeneity Principle after squaring on both sides
[T²] = M⁰L⁰T²
Since 4π²has no dimensions
[m/g] = M L^-1T²
Not obeying Homogeneity Principle, So Equation is Wrong

The centripetal force on a body in circular motion is given by F = mv²/r
a) Write the dimension of force.
b) Using the above formula, write an equation to find % error in centripetal force.
c) What is the number of significant figures in 0.050 N?

a)
   [F] = M L T^-2
b)
   ΔF/F x 100 = Δm/m X 100 + 2 x Δv /v x 100 + Δr/r x 100
c)
     2 Significant figures

a) Suggest a method to measure the diameter of the Moon.
b) Length, breadth and thickness of a block is measured using Vernier callipers. The percentage errors in the measurements are 2%, 1% and 3% respectively. Estimate the percentage error in its volume.
c) A physical quantity is given by h = Fv² / L. F is the force, v is the velocity and L is the angular momentum. Find the dimensions of h .

a) Parallax method
b)
Volume = lbt
Percentage error in Volume
Δv/v x 100 = Δl/l x 100 + Δb/b x 100 + Δt/t x 100 = 2% + 1% + 3 % = 6 %
c)
Dimensions of Angular Momentum [L] = [r P] = =L MLT^-1 = M L² T^-1
[h] = M L T ^-2(L T^-1)² (M L² T^-1) ^-1 = LT^-3

a) The error in the measurement of radius of a circle is 0.6%. Find the percentage error in the calculation of the area of the circle.
b) Name the principle used to check the correctness of an equation.
c) What is the number of significant figures in 0.00820 J?

a) We have Δr/r x 100 = 0.6% area A = πr²
Percentage error inarea ΔA/A x 100 = 2 x Δr/r x 100 = 2 x 0.6% = 1.2%
b) Principle of Homogeneity
c) 3 significant figures

a)Fiqure below shows the paralax method to measure the distance “D” of a planet “S” from the earth. Mark the parallax angle “θ” in the figure. Explain how the distance “D” can be measured.
b) Check whether the equation mv² = mgh is dimentionally correct.

a) θ = <ASB is the Parallax angle

Since Parallax angle is very small,

θ = b/D

Or D = b/θ is the Distance
b)
Use Homogeneity Principle
[mv²] = M ( LT^-1)²= ML²T^-2

[mgh] = M LT^-2 L = ML²T^-2
The equation is Dimensionally correct, even if it is wrong

Select a TRUE statement from the following:
     a) Year and light year have the same dimensions
     b) Intensity of gravitational field has same dimensions as that of acceleration
     c) One angstrom is the mean distance between sun and earth
     d) Parsec is a unit of time.

The accuracy in measurement depends on the limit or the resolution of the measuring instrument
a) State whether the above statement is TRUE or FALSE
b) A physical quantity P is related to four observables a,b,c and d P = a³b²/sqrt(c)d. Percentage errors in measurements of a, b, c and d are 1%, 3%, 2% and 3% respectively. What is the percentage error in the measurement of P ?

a) TRUE
b)
Δp/p x 100 % = 3 x Δa/a x 100 + 2 x Δb/b x 100 + 1/2 x Δc/c x 100 + Δd/d x 100
= 3 x 1% + 2 x 3% + 1/2 x 2 % + 3% = 13 %

The lengths of two bodies measured by a metre scale are l₁ = (20 ± 0.5) cm and l₂ = (15 ± 0.2) cm. Calculate :
a) Sum of these lengths
b) Difference between the lengths.

Sum = (35 ± 0.7) cm
Difference = (5 ± 0.7) cm
Maximum possible Absolute error increases

"Velocity can not be added to temperature "
a) This is in accordance with which law of physics?
b) Check the dimensional correctness of the equation PV = Fx where P is the pressure, V is volume. F is force and x is displacement

(a) Homogeiniety Principal
(b)
[PV] = ML²T^-2
[Fx] = ML²T^-2
Equation is dimensionally correct

The centripetal force on a body of mass m and velocity v moving in a circular orbit of radius r is given by mv²/r.
a) Write the dimensional formula for force
b) Using the formula of centripetal force write an equation to find percentage error in centripetal force.

a) Dimensions of force = MLT^-2
b) Percentage error in centripetal force
ΔF/F x 100 % = Δm/m x 100% + 2 x Δv/v x 100% + Δr/r x 100 %

The volume of water flowing out through a pipe in a given time is V = KA²ut, where A is the area of cross-section of the pipe, u is the speed of flow, t is the time and K is a dimensionless constant.
(a) Name the principle that can be used to check the dimensional correctness of this equation.
(b) Check the correctness of the equation.

(a) Principle of Homogeneity
(b)
[V] = L³
[K] = 1 since K is dimensionless
[KA²ut] = 1 x L² LT^-1 T
= L³ T⁰ = L³
Equation is correct

(a) State the principle of Homogeneity of dimensions.
(b) A planet moves around the Sun in nearly circular orbits. Its period depends on radius (r) of the orbit, mass of the Sun (M) and gravitation constant (G). Derive the expression for its time period of the planet using method of dimensions.