Units & Measurement and Dimensions

The percentage error in the measurement of mass of a body and its speed are $0.73\%$ and $1.84\%$ respectively. The percentage error in the measurement of its momentum and kinetic energy are respectively

A physical quantity $x$ is related as $x = \sqrt{a}\ b^2 c^3 d^{-4}$. Relative errors in the quantities $a$, $b$, $c$ and $d$ are 2%, 1%, 3% and 4% respectively. Relative error in $x$ will be

The voltage across a lamp is $(6.0 \pm 0.3)$ volt and the current passing through it is $(4.0 \pm 0.1)$ ampere. The power consumed in watt will be (using percentage error)

A cuboid has volume $V = l \times l \times \sqrt{l}$, where $l$ is the length of one side. When the length $l$ is measured by a meter scale of least count $1\,\text{mm}$, the relative percentage error in the measurement of its volume is $6....

If two resistors of resistances have values $R_1 = (350 \pm 3)\ \Omega$ and $R_2 = (140 \pm 4)\ \Omega$. The percentage error for the sum and difference of $R_1$ and $R_2$ are respectively

The maximum error in the measurement of the density and mass of the uniform cube are 8% and 2% respectively. Hence, the maximum error in the measurement of length will be

Mass and volume of a body are found to be $(6.00 \pm 0.03)$ kg and $(2.00 \pm 0.02)$ $\text{m}^3$ respectively. Then the density of a body is

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

A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ cm and length $(6 \pm 0.06)$ cm. The maximum percentage error in the measurement of density is

The error in the measurement of length and mass of a cube is 3% and 4% respectively. The error in the measurement of its density will be

The length of rod is measured by meter scale having least count $0.1$ cm and diameter is measured by vernier callipers having least count $0.01$ cm. Length of rod is $5.0$ cm and radius $2.0$ cm. The percentage error in the calculated value...

A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ mm and length $(6 \pm 0.06)$ cm. The maximum error in the measurement of density is

According to Boyle's law, the product PV remains constant. The SI unit of PV is same as that of

The period of oscillation of a simple pendulum is $T = 2\pi (L/g)^{1/2}$. Measured value of 'L' is 10 cm known to 1 mm accuracy and time for 100 oscillations is 50 second, using a watch of 1 second resolution. The percentage error in the me...

The length of a cylinder is measured with a meter rod having least count $0.1$ cm. Its diameter is measured with vernier calipers having least count $0.01$ cm. Length of cylinder is $8.0$ cm and radius is $4.0$ cm. Find the percentage error...

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt{\dfrac{l}{g}}$ where $l$ is about $80$ cm and is known to have $0.1$ cm accuracy. The period is about $1.5$ s. The time of $50$ oscillations is measured by a stop wa...

A quantity P is related as $X^{-2}Y^{-3/2}Z^{2/5}$ where X,Y,Z are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$ respectively in measurement. The maximum fractional error in P is

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...

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

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 \ma...

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

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

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

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 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. T...

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

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}...

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

The formula for the physical quantity is $\mathrm{P}=\frac{\mathrm{x}^3 \mathrm{y}}{\mathrm{z}^2}$ and the percentage error in the determination of physical quantities $\mathrm{x}, \mathrm{y}, \mathrm{z}$ are $0.6 \%, 3 \%$ and $1.3 \%$ res...

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

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

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

Dimensions of Gyromagnetic ratio are

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

The dimensions of self or mutual inductance are given as

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