Grade 11 Physics Quiz - Units & Measurements (Set 4) | Hard

Question 1

A student plots a graph of the square of the time period $T^2$ on the y-axis against the length L of a simple pendulum on the x-axis. If the slope of the resulting straight line is S, what is the physical unit of 1/S?

Accepted Answer

C) $m/s^2$

Answer

A) m/s

Answer

B) $s^2/m$

Answer

D) Unitless

Question 2

In a specific screw gauge, the circular scale has 100 divisions and the pitch is 0.5 mm. When the jaws are closed, the zero of the circular scale is 3 divisions below the reference line. While measuring the diameter of a wire, the linear scale reads 2.5 mm and the 45th division coincides with the reference line. The corrected diameter is:

Accepted Answer

B) 2.740 mm

Answer

A) 2.710 mm

Answer

C) 2.725 mm

Answer

D) 2.695 mm

Question 3

A physical quantity X is represented by the area under a graph of Power (P) vs. Time (t). What is the dimensional formula for $\sqrt{X}$?

Accepted Answer

D) $[ML^2T^{-2}]^{1/2}$

Answer

A) $[ML^2T^{-2}]$

Answer

B) $[MLT^{-1}]$

Answer

C) $[ML^2T^{-1}]$

Question 4

Consider a plot of \ln(y) vs \ln(x) for the equation $y = kx^n$. The slope of this graph is measured to be $1.5 \pm 0.1$. If x is measured with a 2% error, what is the percentage error in y?

Accepted Answer

A) 3.13%

Answer

B) 1.5%

Answer

C) 0.2%

Answer

D) 7.5%

Question 5

A graph of the Thermodynamic Temperature T vs the wavelength of maximum emission $\lambda_m$ for a blackbody is a rectangular hyperbola. The constant of proportionality (Wien's Constant) has dimensions:

Accepted Answer

C) $[L^1 K^1]$

Answer

A) $[L^1 K^{-1}]$

Answer

B) $[L^{-1} K^1]$

Answer

D) $[L^2 K^1]$

Question 6

A non-linear scale is defined such that the reading $R = aV^2 + bV$, where V is the actual voltage. To make the scale dimensionally consistent, what must be the units of a and b if V is in Volts and R is a dimensionless number?

Accepted Answer

A) $a: V^{-2}, b: V^{-1}$

Answer

B) $a: V^2, b: V$

Answer

C) $a: V, b: V^2$

Answer

D) $a: V^{-1}, b: V^{-2}$

Question 7

In a diagram of a Vernier Caliper, 50 divisions of the Vernier scale coincide with 49 divisions of the Main scale. If each Main scale division is 0.5 mm, find the least count.

Accepted Answer

B) 0.01 mm

Answer

A) 0.02 mm

Answer

C) 0.05 mm

Answer

D) 0.001 mm

Question 8

A force F is applied to a body of mass m such that the velocity v varies with time t as $v = kt^2$. The graph of Power P vs time t will be:

Accepted Answer

D) A cubic curve ($P \propto t^3$)

Answer

A) A horizontal straight line

Answer

B) A straight line passing through origin

Answer

C) A parabola opening upwards ($P \propto t^2$)

Question 9

If the density of a cube is determined by measuring its mass and the length of its side, and the maximum error in mass and length are 3% and 2% respectively, the maximum error in density is:

Accepted Answer

C) 9%

Answer

A) 5%

Answer

B) 7%

Answer

D) 12%

Question 10

In a theoretical model, the energy density u of a field is given by $u = \frac{\alpha}{\beta} e^{-\frac{\alpha x}{kT}}$, where x is distance, k is Boltzmann constant, and T is temperature. The dimensions of $\beta$ are:

Accepted Answer

A) $[L^2]$

Answer

B) $[L^3]$

Answer

C) $[ML^2T^{-2}]$

Answer

D) $[M^0L^0T^0]$

Question 11

A visual representation shows a cylinder of radius $r = (5.0 \pm 0.1)cm$ and height $h = (10.0 \pm 0.1)cm$. The percentage error in its volume V is approximately:

Accepted Answer

B) 5%

Answer

A) 4%

Answer

C) 3%

Answer

D) 2%

Question 12

A graph of $\log_{10}(F)$ vs $\log_{10}(a)$ for a particle of constant mass m (where F = ma) is:

Accepted Answer

D) A straight line with slope 1

Answer

A) A parabola

Answer

B) A straight line with slope $\log m$

Answer

C) A straight line with intercept 0

Question 13

If the units of Length and Force are increased four times, the unit of energy will increase:

Accepted Answer

C) 16 times

Answer

A) 4 times

Answer

B) 8 times

Answer

D) 32 times

Question 14

Consider the following measurement: L = 2.331cm, B = 2.1cm. The value of L+B with regard to significant figures is:

Accepted Answer

A) 4.4 cm

Answer

B) 4.43 cm

Answer

C) 4.431 cm

Answer

D) 4.5 cm

Question 15

A student measures the period of oscillation of a pendulum. The readings are 2.63s, 2.56s, 2.42s, 2.71s and 2.80 s. The mean absolute error is:

Accepted Answer

B) 0.108 s

Answer

A) 0.11 s

Answer

C) 0.20 s

Answer

D) 0.05 s

Question 16

Which of the following pairs of physical quantities has a ratio with dimensions $[L^2T^{-2}]$?

Accepted Answer

C) Latent Heat and (Dimensionless constant)

Answer

A) Force and Mass

Answer

B) Work and Time

Answer

D) Pressure and Density

Question 17

A certain physical quantity is calculated as $Y = a^2b^3/c\sqrt{d}$. If the percentage errors in a, b, c, d are 1%, 2%, 3%, 4% respectively, the percentage error in Y is:

Accepted Answer

D) 13%

Answer

A) 10%

Answer

B) 12%

Answer

C) 7%

Question 18

In the formula $V = \frac{\pi P r^4}{8 \eta l}$, where V is volume flow rate, P is pressure difference, r is radius, l is length. The dimensions of coefficient of viscosity \eta are:

Accepted Answer

A) $[ML^{-1}T^{-1}]$

Answer

B) $[ML^{-1}T^{-2}]$

Answer

C) $[MLT^{-1}]$

Answer

D) $[M^0L^0T^0]$

Question 19

In a graph of Velocity (v) vs. Displacement (x) for a particle performing SHM, the area enclosed by the elliptical plot has units of:

Accepted Answer

B) $m^2/s$

Answer

A) $m^2/s^2$

Answer

C) $m/s^2$

Answer

D) $m^2s$

Question 20

The time t of oscillation of a gas bubble from an explosion under water depends on Static Pressure P, Density of water d, and Total Energy E. If $t \propto P^a d^b E^c$, the values of a, b, c are:

Accepted Answer

C) -5/6, 1/2, 1/3

Answer

A) 5/6, -1/2, 1/3

Answer

B) -5/6, 1/2, 1/2

Answer

D) 1/2, 1/2, 1/2