JEE Units and Measurements PYQs with Video Solutions PDF

Keeping tl1e significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is:

Consider a modified Bernoulli equation.
$$\left( P + \frac{A}{B t^2} \right) + \rho g (h + B t) + \frac{1}{2}\,\rho V^2 = \text{constant}$$
If t has tile dimension of time then the dimensions of A and B are ___.___ respectively.

In an experiment the values of two spring constants were measured as $$k_{1}=(10\pm0.2)N/m\text{ and }k_{2}=(20\pm0.3)N/m$$. lf these springs are connected in parallel, then the percentage error in equivalent spring constant is :

If $$\epsilon$$, E and t represent the free space permittivity, electric field and time respectively, then the unit of $$ \frac{\epsilon E}{t}$$ will be :

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25cm. The relative error in the measurement of average length of the rod is :

Match the LIST-I with LIST-II

Choose the correct answer from the options given befow:

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Which one of the following is not a measurable quantity ?

The time period of a simple harmonic oscillator is $$T=2\pi \sqrt{\frac{k}{m}}$$. Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is________%.

Matd1 List - I with List - II.
List - I                                          List - II
A. Coefficient of viscosity          I.   $$[ML^{-1}T^{-2}]$$
B. Surface tension                      II.   $$[ML^{2}T^{-2}]$$
C. Pressure                                  III.  $$[ML^{0}T^{-2}]$$
D. Surface energy                       IV.  $$[ML^{-1}T^{-1}]$$
Choose the correct answer from the options given below:

In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrwnent used in recording these readings is ___ mm.

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire $$=(0.60 \pm 0.003)g$$ radius of wire $$=(10.00 \pm 0.05)cm$$]

If B is magnetic field and $$\mu_o$$ is permeability of free space, then the dimensions of $$(B/\mu_o)$$ is

The energy of a system is given as $$E(t)=\alpha^{3}e^{-\beta t}$$, where t is the time and $$\beta= 0.3s^{-1}$$. The errors in the measurement of $$\alpha$$ and t are 1.2% and 1.6%, respectively. At t=5s,maximum percentage error in the energy is:

Match List - I with List - II.

Choose the correct answer from the options given below :

For an experimental expression $$y=\frac{32.3\times125}{27.4},$$ where all the digits are significant. Then to report the value of  $$y$$  we should write:

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $$[M^{a}L^{b}T^{c}]$$. If b=-3 the value of c is___________

The expression given below shows the variation of velocity $$(\upsilon)$$ with time $$(t),\upsilon = At^{2}+\frac{Bt}{C+t}$$. The dimension of ABC is :

The pair of physical quantities not having same dimensions is :

The position of a particle moving on x-axis is given by $$x(t)=A\sin t+B\cos^{2}t+Ct^{2}+D$$, where is time. The dimension of $$\frac{ABC}{D}$$ is

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions $$[ML^{2}T^{-2}]$$
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

Match List - I with List - II.

Choose the correct answer from the options given below :

Match List - I with List - II.

A physical quantity Q is related to four observables a,b,c,d as follows : $$Q = \frac{ab^{4}}{cd}$$ where, $$a = (60 \pm 3)\,\text{Pa}$$; $$b = (20 \pm 0.1)\,\text{m}$$; $$c = (40 \pm 0.2)\,\text{Nsm}^{-2}$$; and $$d = (50 \pm 0.1)\,\text{m}$$ , then the percentage error in Q is $$\frac{x}{1000}$$ , where x = ________ .

In an experiment to measure focal length (f) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $$\Delta u$$ and $$\Delta v$$, respectively. The error in the measurement of the focal length of the convex lens will be:

The equation of stationary wave is: $$y = 2a\sin\left(\frac{2\pi nt}{\lambda}\right)\cos\left(\frac{2\pi x}{\lambda}\right)$$. Which of the following is NOT correct:

Match List - I with List - II.

The radius $$r$$, length $$l$$ and resistance $$R$$ of a metal wire was measured in the laboratory as $$r = 0.35 \pm 0.05$$ cm, $$R = 100 \pm 10$$ ohm, $$l = 15 \pm 0.2$$ cm. The percentage error in resistivity of the material of the wire is :

The dimensional formula of angular impulse is :

With rise in temperature, the Young's modulus of elasticity

$$10$$ divisions on the main scale of a Vernier calliper coincide with $$11$$ divisions on the Vernier scale. If each division on the main scale is of $$5$$ units, the least count of the instrument is :

Match List - I with List - II.

Choose the correct answer from the options given below:

Given below are two statements:

Statement (I) : Planck's constant and angular momentum have the same dimensions.

Statement (II) : Linear momentum and moment of force have the same dimensions. In light of the above statements, choose the correct answer from the options given below :

Identify the physical quantity that cannot be measured using spherometer :

The equation of state of a real gas is given by $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$, where $$P$$, $$V$$ and $$T$$ are pressure, volume and temperature respectively and $$R$$ is the universal gas constant. The dimensions of $$\frac{a}{b^2}$$ is similar to that of :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the correct answer from the options given below :

The resistance $$R = \frac{V}{I}$$, where $$V = (200 \pm 5)$$ V and $$I = (20 \pm 0.2)$$ A, the percentage error in the measurement of $$R$$ is :

A physical quantity $$Q$$ is found to depend on quantities $$a, b, c$$ by the relation $$Q = \frac{a^4 b^3}{c^2}$$. The percentage error in $$a, b$$ and $$c$$ are $$3\%, 4\%$$ and $$5\%$$ respectively. Then, the percentage error in $$Q$$ is:

Match List-I with List-II.

If mass is written as $$m = kc^{P}G^{-1/2}h^{1/2}$$, then the value of $$P$$ will be : (Constants have their usual meaning with $$k$$ a dimensionless constant)

If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:

If the percentage errors in measuring the length and the diameter of a wire are $$0.1\%$$ each. The percentage error in measuring its resistance will be:

A force is represented by $$F = ax^2 + bt^{1/2}$$, where $$x$$ = distance and $$t$$ = time. The dimensions of $$\frac{b^2}{a}$$ are :

Consider two physical quantities $$A$$ and $$B$$ related to each other as $$E = \frac{B - x^2}{At}$$ where $$E$$, $$x$$ and $$t$$ have dimensions of energy, length and time respectively. The dimension of $$AB$$ is

Applying the principle of homogeneity of dimensions, determine which one is correct, where $$T$$ is time period, $$G$$ is gravitational constant, $$M$$ is mass, $$r$$ is radius of orbit.

What is the dimensional formula of $$ab^{-1}$$ in the equation $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$, where letters have their usual meaning.

A vernier callipers has 20 divisions on the vernier scale, which coincides with $$19^{th}$$ division on the main scale. The least count of the instrument is $$0.1$$ mm. One main scale division is equal to ______ mm.

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $$4.62 \text{ s}, 4.632 \text{ s}, 4.6 \text{ s}$$ and $$4.64 \text{ s}$$. The arithmetic mean of these readings in correct significant figure is :

Match List I with List II :

(Where $$a$$ = radius of planet orbit, $$r$$ = radius of planet, $$M$$ = mass of Sun, $$m$$ = mass of planet)