General Physics Numerical

General Physics Numerical

1)A physical quantity Q is related to four observables x, y, z and t by the relation
Q = 𝑥^2/5𝑧3𝑦 𝑡
The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5% and 1% respectively. Find the percentage error in Q.

2) The length and breadth of a rectangle are (5.7 ± 0.1)cm and (3.4 ± 0.2)cm. Find the error in area of rectangle with limited error.

3) The dimension of 12 Є₀E^2 (Є₀=permittivity of free space, E = Electric field) is.

4) If are A, velocity V and density ρ are base units, then find the dimensional formula of force.

5) To find the value of g using simple pendulum, T =(2 ± 0.01)sec and l = (50 ± 0.1)cm was measured. Find the maximum percentage error in g.

6) A wire has a length l = (6 ± 0.06)cm, radius r =(0.05 ± 0.005)cm and mass m = (0.3 ± 0.003)gm. Find the maximum error in the density of wire.

7) The density of a sphere is measured by measuring its mass and diameter. If it is known that the maximum percentage error in the measurement is 2% and 3%. Find the maximum percentage error in the measurement of density.

8) Find the maximum and minimum value of the functions –
a) y = 25x^2 + 5 -10x                                                     b) y = 9 – (x – 3)2
c) y = (sin 2x – x) where, −𝜋2 < x < 𝜋2                   d) y = x^3 – 6x^2 + 9x +15
e) y = 5 – (x – 1)^2

9) If the error in measurement of radius of a sphere is 1%. Find the error in measurement of volume.

10) If the momentum of particle is increased by 100%.Find the percentage increase in the kinetic energy of the particle.

11) By what percentage should the pressure of a given mass of a gas be increased, so as to decrease its volume by 10% at a constant temperature.

12) Percentage error in the measurement of mass and velocity are 2% and 3% respectively. Find the error in the estimate of kinetic energy obtained by measuring mass and velocity.

13) The radius of a sphere is measured to be (2.1 ± 0.5)cm. Calculate its surface area with limit error.

14) The value of gravitation constant G = 6.67 x 10-11 Nm^2/kg^2 in S.I units. Convert it into CGS unit.

15) A force is given by F= at + bt^2, where t is the time. Find the dimension of a and b.

16) The velocity v of a particle is given by
V = at + 𝑏𝑡+𝑐 , where a, b and c are constant.
Find the dimension of a, b and c.

17) Find the dimension of 𝑎𝑏 in the equation P = 𝑎−𝑡^2𝑏𝑥 , where P is pressure, x is distance and t is time.

18) Find the physical quantity whose dimension is [ M^-1 L^-3 T^3A^2 ].

19) Young’s modulus of steel is 2.0 x 1011 N/m^2. Express it into dyne/cm2.

20) In the expression y = a sin(ωt +θ), y is the displacement and t is time. Write the dimension of a, ω and θ.

21) Charge on the capacitor is given by Q = Iα𝑒−𝐼𝑡Δ𝑣Є°𝛽 , where β and α are constants. t=time, I = current , Δv= potential difference. Find the dimension of 𝛽𝛼 .

22) Find the percentage error in the expression x = 𝑎𝑏^2𝑐^3. If the percentage error in a, b and c are ±1%, ±3% and ±2% respectively.

23) The momentum of an electron in an orbit is h/λ, where h is plank’s constant and λ is the wavelength associated with it. The nuclear magnetron of electron of charge e and mass me is given as
μn = 𝑒ℎ3672𝜋𝑚𝑒.
Find the dimension of μn .

24) Intensity observed in an interference pattern is I = I₀ sin2θ. At θ = 30° intensity I =5 ± 0.0020 W/m2. Find percentage error in angle if I₀ = 20 W/m2.

25) The length of string of a simple pendulum is measured with a meter scale to be 90 cm. The radius of a bob plus the length of hook is calculated to be 2.13 cm using measurement with a side calipers. What is the effective length of the pendulum? {This effective length is defined as the distance between the point of suspension and the centre of the bob}

26) Vernier calipers has 20 divisions on its vernier scale which coincide with 19 divisions on the main scale. Least count of the instrument is 0.1mm. Find the main scale division.

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