In an experiment, mass of an object is measured by applying a kno… - Vidyadip

MCQ

In an experiment, mass of an object is measured by applying a known force on it, and then measuring its acceleration. If in the experiment, the measured values of applied force and the measured acceleration are $F=10.0 \pm 0.2 \,N$ and $a=1.00 \pm 0.01 \,m / s ^2$, respectively. Then, the mass of the object is ............... $kg$

A
$10.0$
B
$10.0 \pm 0.1$
✓
$10.0 \pm 0.3$
D
$10.0 \pm 0.4$

✓

Answer

Correct option: C.

$10.0 \pm 0.3$

c
(c)

As, force $F=m a$

$\Rightarrow \frac{\Delta F}{F}=\frac{\Delta m}{m}+\frac{\Delta a}{a} \Rightarrow \frac{\Delta m}{m}=\frac{\Delta F}{F}-\frac{\Delta a}{a}$

$\Rightarrow \frac{\Delta m}{m}=\left(\frac{\pm 0.2}{10}\right)-\left(\frac{\pm 0.01}{1}\right)$

So, $\left(\frac{\Delta m}{m}\right)_{\max }=\frac{0.2}{10}+\frac{0.01}{1}=0.03$

Maximum error in mass occurs when error in force and acceleration are of different signs.

So, $\Delta m=0.03 \times m=0.03 \times 10 \Rightarrow \Delta m=0.3\, kg$

Hence, mass of object is $m=10 \pm 0.3 \,kg$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. units,dimensions and measurement→1. units,dimensions and measurement — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A ball is projected with kinetic energy $E$ at an angle of ${45^o}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

If $Q= \frac{X^n}{Y^m}$ and $\Delta X$ is absolute error in the measurement of $X,$ $\Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is

The total energy of particle performing $\text{S.H.M.}$ is depends on:

A simple pendulum of length $ l$ has a brass bob attached at its lower end. Its period is $T$. If a steel bob of same size, having density $ x$ times that of brass, replaces the brass bob and its length is changed so that period becomes $2T$, then new length is

The graph between two temperature scales $A$ and $B$ is shown in between upper fixed point and lower fixed point there are $150$ equal division on scale $A$ and $100$ on scale $B$. The relationship for conversion between the two scales is given by:

Select the correct alternative$(s)$

A block $'A'$ of mass $M$ moving with speed $u$ collides elastically with block $B$ of mass $m$ which is connected to block $C$ of mass $m$ with a spring. When the compression in spring is maximum the velocity of block $C$ with respect to block $A$ is (neglect friction)

A man standing on a cliff claps his hand hears its echo after $1 \,sec$. If sound is reflected from another mountain and velocity of sound in air is $340\, m/sec.$ Then the distance between the man and reflection point is ..... $m$

A packet contains silver powder of mass $20.23 \,g \pm 0.01 \,g$. Some of the powder of mass $5.75 \,g \pm 0.01 \,g$ is taken out from it. The mass of the powder left back is ................

Variation of atmospheric pressure, with height from earth is ................