131.
In a vernier callipers $$N$$ divisions of vernier scale coincide with $$N - 1$$ divisions of main scale (in which length of one division is $$1\,mm$$ ). The least count of the instrument should be
133.
The current voltage relation of a diode is given by $$I = \left( {{e^{1000V/T}} - 1} \right)mA,$$ where the applied voltage $$V$$ is in volts and the temperature $$T$$ is in degree kelvin. If a student makes an error measuring $$ \pm 0.01\,V$$ while measuring the current of $$5\,mA$$ at $$300\,K,$$ what will b the error in the value of current in $$mA$$ ?
134.
Distance travelled by a particle at any instant $$'t'$$ can be represented as $$S = A\left( {t + B} \right) + C{t^2}.$$ The dimensions of $$B$$ are
we know that the velocity of light in vacuum is given by
$$\eqalign{
& c = \frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }} \cr
& \therefore \frac{1}{{{\mu _0}{\varepsilon _0}}} = {c^2} = {L^2}{T^{ - 2}} \cr} $$
136.
In equation, $$r = {m^2}\sin \pi t,$$ where $$t$$ represents time. If the unit of $$m$$ is $$N,$$ then the unit of $$r$$ is
Least count of a screw gauge $$ = \frac{{{\text{Pitch}}}}{{{\text{Number of circular scale divisions}}}}$$
$$\eqalign{
& = \frac{{1\,mm}}{{50}} \cr
& = 0.02\,mm \cr} $$
Therefore the pitch and no. of circular scale divisions are $$1\,mm$$ and 50 respectively.
138.
Which of the following statements is/are correct?
1. 345.726 has six significant figures.
2. 0.004289 has seven significant figures.
3. 125000 has three significant figures.
4. 9.0042 has five significant figures.
139.
The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {\frac{L}{g}} .$$ Measured value of $$L$$ is $$20.0 \,cm$$ known to $$1 \,mm$$ accuracy and time for $$100$$ oscillations of the pendulum is found to be $$90s$$ using a wrist watch of $$1s$$ resolution. The accuracy in the determination of $$g$$ is-
140.
If $$x = at + b{t^2},$$ where $$x$$ is the distance travelled by the body in kilometer while $$t$$ is the time in second, then the unit of $$b$$ is
As $$x = at + b{t^2}$$
According to the concept of dimensional analysis and principle of homogeneity
$$\eqalign{
& \therefore \,{\text{unit}}\,{\text{of}}\,x = {\text{unit}}\,{\text{of}}\,b{t^2} \cr
& \therefore \,{\text{unit}}\,{\text{of}}\,b = \frac{{{\text{unit}}\,{\text{of}}\,x}}{{{\text{unit}}\,{\text{of}}\,{t^2}}} = km/{s^2} \cr} $$