Units & measurements practice · Mixed difficulty

The equation of the stationary wave is $y=2 a \sin \left(\frac{2 \pi c t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$, which of the following statements is wrong

Assertion: Dimensions of coefficient of viscosity are $\left[M L^{-1} T^{-1}\right]$
Reason: Coefficient of viscosity is force acting per unit area per unit velocity gradient

A student makes 10 one-second measurements of the disintegration of a sample of a long-lived radioactive isotope and obtained the following values $3,0,2,1,2, 4,0,1,2,5$. How long should the student want to establish the rate to an uncertainity of 1 per cent? (Given standard deviation of count rate of a radioactive decay $=\sqrt{\text { mean decay rate)}}$

If $R, X_{L}$ and $X_{c}$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless

The dimensions of electric dipole moment are

1 Parsec is equal to

Assertion: The number of significant figures in 0.001 is 1 .

Reason: All zeros to the right of a decimal point and to the left of a non-zero digit are never significant.

Force ${F}$ depends on distance $(x)$ and time $(t)$ as $F=a x^2+b t^{\frac{1}{2}}$, find dimension of $\frac{b^2}{a}$

Unit of reduction factor is

The physical quantity which has dimensional formula as that of $\frac{{\mathrm{Energy}}}{{\mathrm{Mass}\,\,\,\mathrm{ \times }\,\,\,\mathrm{Length}}}$ is

Which of the following physical quantities do not have same dimensions?

Which of the following is a dimensional constant?

In the equation ${S_{nth}}$ the $= u + \frac{a}{2}\left( {2n - 1} \right),$ the letters have their usual meanings. The dimensional formula of ${S_{nth}}$ is

Dimensional formula of angular momentum is:

Assertion: The physical quantities different in nature but having the same dimensions must possess the same units.

Reason: If the dimensions of two physical quantities are same, their units must also be same.

In a new system of unit, 1 unit of mass is $10 \mathrm{~kg}, 1$ unit of length is $10 \mathrm{~m}$ and 1 unit of time is $1 \mathrm{~s}$. If 1 unit of power in this unit is equal to $x$ Watt, find $x$.

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is:

If $P=P_0 e^{-\left[\frac{\alpha t}{x+\beta}\right]}$, where $t$ is time and $x$ is displacement. Then dimension of $\left[\frac{\alpha^2}{\beta}\right]$ is same as

In two systems of relations among velocity, acceleration and force are respectively $v_2=\frac{\alpha^2}{\beta} v_1$, $a_2=\alpha \beta a_1$ and $F_2=\frac{F_1}{\alpha \beta}$. If $\alpha$ and $\beta$ are constants then relations among mass, length and time in two systems are

In a new system of units, unit of mass is taken as 10 $\mathrm{kg}$, unit of length is $60 \mathrm{~m}$ and unit of time is 1 minute. The value of $20 \mathrm{~N}$ weight of a body in the new unit will be

Light year is used to measure which among the following.

The number of the significant figures in $1111.8 \times {10^{11}}$ is

If e is the charge, $\mathrm{V}$ the potential difference, $\mathrm{T}$ the temperature, then the units of $\frac{\mathrm{eV}}{\mathrm{T}}$ are the same as that of

Which of the following the same dimensions ?

Write the order of magnitude of the following measurements:

(i) $25,710,000 \mathrm{~m}$
(ii) $0.00000521 \mathrm{~kg}$.

Assertion : Light year and year, both measure time.

Reason : Because light year is the time that light takes to reach the earth from the sun.

The unit of impulse is the same as that of

If the displacement of y of a particle is $y = A\sin (pt + qx)$ then dimensional formula of $Apq$ is

The power of lens is $P = \frac{1}{f},\;$ where f is focal length of the lens . The dimensions of power of lens are

If ${a}=8 \pm 0.08$ and ${b}=6 \pm 0.06$, Let ${x}={a}+{b}, {y}={a}-{b}, {z}={a} \times {b}$. The correct order of $\%$ error in ${x}, {y}$ and ${z}$