Unit of reduction factor is

(a)

ampere

(b)

ohm

(c)

tesla

(d)

weber

The dimensions of impulse are equal to that of

(a)

force

(b)

linear momentum

(c)

pressure

(d)

angular momentum

Dimensions of relative density is 

(a)

\(\left[ { M }^{ }{ L }^{- 2 } \right] \)

(b)

\(\left[ { M }^{ }{ L }^{ -3 } \right] \)

(c)

dimensionless

(d)

\(\left[ { M }^{ 2 }{ L }^{-6 } \right] \)

The number of significant figures in \(11.118\times { 10 }^{ -6 } V\) is

(a)

3

(b)

4

(c)

5

(d)

6

The values of two resistors are \(\left( 5.0\pm 0.2 \right) ㏀\) and \(\left( 10.0\pm 0.1 \right) ㏀\). What is the percentage error in the equivalent resistance when they are connected in parallel?

(a)

2%

(b)

5%

(c)

7%

(d)

10%

A quantity is given by \(X=\frac { { \varepsilon }_{ 0 }lV }{ t } \), where V is the potential difference and l is the length. Then, X has dimensional formula same as that of 

(a)

resistance

(b)

charge

(c)

voltage

(d)

current

The unit of specific conductivity is

(a)

\({ \Omega -cm }^{ -1 }\)

(b)

\({ \Omega -cm }^{ -2 }\)

(c)

\({ \Omega^{ -1 } -cm }\)

(d)

\(\)\({ { \Omega }^{ -1 }-cm }^{ -1 }\)

The radius of a circle is 2.12 m. Its area according to the rule of significant figures is

(a)

14.1124 m² 

(b)

14.112 m²

(c)

14.11 m²

(d)

14.1 m²

The length of a uniform rod is 100.0 cm. If length is measured with a meter rod having least count 1 mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder is

(a)

2.1%

(b)

3%

(c)

2.01%

(d)

3.2%

If the absolute errors in two physical quantities A and B are a and b respectively, then the absolute error in the value of A-B is

(a)

b-a

(b)

a\(\neq \)b

(c)

a+b

(d)

a-b

The dimensional formula of the constant "a" in Vanderwaals gas equation is \((p+{a\over v^2})(v-b)=RT\)

(a)

MT⁵T^-2

(b)

ML³T^-2

(c)

ML²T^-1

(d)

ML⁵T^-3

Identify the pair of physical quantities having the same dimensions.

(a)

Light year and period of a pendulum

(b)

Angular momentum and torque

(c)

Energy and Modulus of elasticity

(d)

Torque and work

A ratio signal sent towards the distant planet, returns after "t"s. If "c" is the speed of radio waves then the distance of the planet and from the earth is______________.

(a)

\(c\frac{t}{2}\)

(b)

ct²

(c)

2ct

(d)

\(c^2\frac{t^2}{2}\)

One atomus equal to ____________.

(a)

100 ms

(b)

\(\frac { 1 }{ 6.25 } \) ms

(c)

160 ms

(d)

160 ms

The mean radius of a wire is 2 mm. Which of the following measurements is most accurate?

(a)

1.9 mm

(b)

2.25 mm

(c)

2.3 mm

(d)

1.83 mm

Having all units in atomic standards is more useful. Explain.

Find the SI unit of moment of inertia. 5.64 kg mass of a object is moving uniformly. The radius of gyration is measured as 30cm of an object. Then what is the moment of Inertia?

Can a quantity have units but still be dimensionless?

Round off the following numbers as indicated 19.45 up to 3 digits

In a physical units, how many units are there in 1 metre?
1 Astronomical unit (AU = 1.496\(\times\)10¹¹ m)
Given data:
1 AU = 1.496\(\times\)10¹¹m
1 ly = 9.467 x \(\times\)10¹⁵m
1 mm = 10^-6m
1 parsec = 3.08\(\times\)10¹⁶m

In a physical units, how many units are there in 1 metre?
1 micron (\(\mu\)) = 10^-6 m
Given data:
1 AU = 1.496\(\times\)10¹¹m
1 ly = 9.467\(\times\)10¹⁵m
1 mm = 10^-6m
1 parsec = 3.08\(\times\)10¹⁶m

Show that \(({P}^{-5/6}{ρ}^{1/2}{E}^{1/3})\) is of the dimension of time. Here P is the pressure, \(ρ\) is the density and E is the energy of a bubble)

The parallal x of a heavenly body measured from two points diametrically opposite on equator of earth is 2'. Calculate the distance of the heavenly body. [Given radius of the earth = 6400 km] [1" = 4.85\(\times\)10^-6 rad]

The length of a rod as measured in an experiment was found to be 2.48 m, 2.46 m, 2.49 m, 2,50 m and 2.48 m. Find the average length, absolute error and percentage error. Express the result with error limit.

The length of a rod as measured in an experiment was found to be 3.48m, 3.46m, 3.49m, 3.50m and 3.48 m. Find the average length, the absolute error in each observation and the percentage error.

In a series of successive measurements in an experiment, the readings of the period of oscillation of a simple pendulum were found to be 2.63s, 2.56s, 2.42s, 2.71s, and 2.80s.
Calculate
(i) the mean value of the period of oscillation
(ii) the absolute error in each measurement
(iii) the mean absolute error
(iv) the relative error
(v) the percentage error.
(vi) Express the result in proper form.