Units & Measurement and Dimensions · Physics · MHT CET

A physical quantity ' X ' is related to four measurable quantities ' $a$ ', ' $b$ ', ' $c$ ' and ' $d$ ' as $\mathrm{X}=\mathrm{a}^2 \mathrm{~b}^3 \mathrm{c}^{5 / 2} \mathrm{~d}^{-2}$. The percentage error in the measurement of 'a', 'b', 'c' and 'd' are $1 \%$, $2 \%, 2 \%$ and $4 \%$ respectively. The percentage error in measurement of quantity ' X ' is

In an experiment four quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are measured with percentage $3 \%, 2 \%, 3 \%$ and $1 \%$ respectively. Quantity ' $A$ ' is calculated as follows

$\mathrm{A}=\frac{\mathrm{pq}^2}{\mathrm{r}^2 \mathrm{~s}^4}$, the percentage error in ' A ' is

The error in the measurement of length and mass is $3 \%$ and $4 \%$ respectively. The error in the measurement of density will be

A force F is applied on a square plate of side L . If the percentage error in determining F is $3 \%$ and that in L is $2 \%$, then the percentage error in determining the pressure is

A wire has a mass $0.3 \pm 0.003$ gram, radius $0.5 \pm 0.005 \mathrm{~mm}$ and length $6 \pm 0.06 \mathrm{~cm}$. The maximum percentage error in the measurement of its density is

The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively $4 \%$ and $2 \%$, the percentage error in the measurement of pressure is

Which of the following comes under the category of random errors?

The percentage error in the measurement of mass and speed of a particular body is $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is

The period of oscillating simple pendulum is $\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$ where length ' $l$ ' is 100 cm with error 1 mm . Period is 2 second. The time of 100 oscillations is measured by a stopwatch of least count 0.1s. The percentage error in gravitational acceleration ' g ' is

Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is

A physical quantity A can be determined by measuring parameters $\mathrm{B}, \mathrm{C}, \mathrm{D}$ and E using the relation $A=\frac{B^a C^\beta}{D^\gamma E^\delta}$. If the maximum errors in the measurement are $\mathrm{b} \%, \mathrm{c} \%, \mathrm{~d} \%$ and $\mathrm{e} \%$ then maximum error in the value of A is

The density of a cube is measured by measuring its mass and length of its sides. The \% error in the measurement of mass and length are $5 \%$ and $6 \%$ respectively. The percentage error in the measurement of density is

A student measures time for 20 oscillations of a simple pendulum as $30 \mathrm{~s}, 32 \mathrm{~s}, 35 \mathrm{~s}$ and 35 s . If the minimum division in the measuring clock is 1 s , then correct mean time (in second) is

The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2){ }^{\circ} \mathrm{C}$ and $(82.3 \pm 0.3){ }^{\circ} \mathrm{C}$. The rise in temperature with proper error limits is

If $L$ is the inductance and $R$ is the resistance then the SI unit of $\frac{L}{R}$ is

Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are

Let $x=\pi R\left(\frac{P^2-Q^2}{2}\right)$, where $P, Q$ and $R$ are lengths. The physical quantity $x$ is

Let force $$F=A \sin (C t)+B \cos (D x)$$, where $$x$$ and $$t$$ are displacement and time, respectively. The dimensions of $$\frac{C}{D}$$ are same as dimensions of

$\left[\mathrm{L}^2 \mathrm{M}^1 \mathrm{~T}^{-2}\right]$ are the dimensions of

The force ' $F$ ' acting on a body of density ' $d$ ' are related by the relation $F=\frac{y}{\sqrt{d}}$. The dimensions of ' $y$ ' are

The dimensions of self or mutual inductance are given as

The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of

Dimensions of Gyromagnetic ratio are