The measured value of the length of a simple pendulum is $$20\mathrm{cm}$$ with $$2\mathrm{mm}$$ accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $$\mathrm{N}\%$$. The value of $$\mathrm{N}$$ 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 $$F=a{x}^2+b{t}^{\frac{1}{2}}$$ where $$x=$$ distance and $$t=$$ time. The dimensions of $$b^2/a$$ are:

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

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $$0.5\mathrm{mm}$$, the Vernier constant of traveling microscope is

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

Match List I with List II. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II (A) Coefficient of viscosity (I) $$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$$ (B) Surface tension (II) $$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$$ (C) Angular momentum (III) $$\left[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\right]$$ (D) Rotational kinetic energy (IV) $$\left[\mathrm{M}{\mathrm{L}}^0{\mathrm{T}}^{-2}\right]$$ Choose the correct answer from the options given below :

The de-Broglie wavelength associated with a particle of mass $$m$$ and energy $$E$$ is $$h/\sqrt{2mE}$$. The dimensional formula for Planck's constant is :

The dimensional formula of latent heat is :

One main scale division of a vernier caliper is equal to $$\mathrm{m}$$ units. If $${\mathrm{n}}^{\text{th }}$$ division of main scale coincides with $$(n+1{)}^{\text{th }}$$ division of vernier scale, the least count of the vernier caliper is :

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

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.

If $${ϵ}_{\mathrm{o}}$$ is the permittivity of free space and $$\mathrm{E}$$ is the electric field, then $${ϵ}_{\mathrm{o}}{\mathrm{E}}^2$$ has the dimensions :

There are 100 divisions on the circular scale of a screw gauge of pitch $$1\mathrm{mm}$$. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

Least count of a vernier caliper is $$\frac{1}{20\mathrm{N}}\mathrm{cm}$$. The value of one division on the main scale is $$1\mathrm{mm}$$. Then the number of divisions of main scale that coincide with $$\mathrm{N}$$ divisions of vernier scale is :

In an expression $$a\times 10^b$$ :

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1\mathrm{mm}$$. The main scale reading is $$2\mathrm{cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $$\mathrm{g}$$, the density of the sphere is:

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

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