14%

5.67 x 10^-8 Js^-1m^-2K^-4

3.46 x 10⁶m

No, the statement is true

2.000cm is most accurate because it is correct upto third place of a decimal.

No, the inertial and gravitational mass of a body are equivalent.

Mass spectrograph.

Hence, length of the arc = ?
Radius = 31.0 cm, θ=π/6
From, legnth of the arc of a circle(l) = rθ
31.0 × π/6 = 16.2cm

Both bar and torr are the units of pressure.
1 bar = 1 atmospheric pressure = 760 mm of Hg column
= 10⁵N/m²
1 torr = 1mm of Hg column
1 bar = 760 torr

In 1 teragram = 10¹²g
In 1 metric ton = 10³kg = 10³ x 10³ = 10⁶g
Number of metric tons are in teragram
\(\frac { { 10 }^{ 12 }g }{ { 10 }^{ 6 }g } ={ 10 }^{ 6 }\)

Given, Area of object = 1.75 x 10^-4 m²
Area of image = 1.55 m²
Areal magnification = \(\frac { Area\ of\ image }{ Area\ of\ object } \)
\(\frac { 1.55 }{ 1.74X{ 10 }^{ -4 } } \approx 8857\)
Linear magnification = \(\sqrt { \text{A real maginification} } \)
\(=\sqrt { 8857 } \)
= 94.1

Given, Magnification of microscope = 100
Observed width of the hair = 3.5 mm
Estimates on the thickness of hair is given by,
Magnification = \(\frac { observed \ width }{ Real \ width } \)
or Real width =   \(\frac { Observed\ width }{ Magnification } =\frac { 3.5 }{ 100 } \)
= 0.035 mm

Acceleration = (10 m/(1s)²) 
= (10 x 10^-3 / [1/60 x 60])²
= (3600)² x 10^-2 km/h²
= 1.29 x 10⁵ km/h².

Weight of diamond = 5.42 g = 0.00542 Kg
Total weight = 1.2 + 0.00542
= 1.20542 kg = 1.2 kg

One Barn is a small unit of area used to measure area of nuclear cross-section
∴ 1 barn = 10^-28 m².

True, because human heart beats at a regular rate.

1 amu =1.66 x 10^-27 kg
∴ 1 kg = (1/1.66 x 10^-27) amu = 0.6 x 10²⁷ amu

1 m = 6.67 x 10^-12 AU

No, since length is fundamental quantity and velocity is the derived quantity.

Step 1, Given data
1 micro century =10−6×100 years
Step 2, Converting in micro century
We know that in one year there are 365 days and in one day there are 24 hours. In 1 hour there are 60 minutes.
So converting i micro century in minute
=10⁻⁴ × 365 × 24 × 60 min
Now we can write,
100 min=\(= \frac{1}{10^{−4}×365×24×60}×100\)
\(=\frac{10^5}{365×144}\)
=1.9 microcenturies
Hence in the micro century the time period is written as 1.9 micro centuries.

Here, r =41.3 fermi \(=41.3 \times 10^{15} \mathrm{~m}, V=\) ?
\(V  =\frac{4}{3} \pi r^3=\frac{4}{3} \times 3.14\left(41.3 \times 10^{15}\right)^3 \)
\(=2.85 \times 10^{40} \mathrm{~m}^3\)
= 2.95 x 10^-40m³

Given, l = \((10.5\pm 0.2)\)cm, b = \((5.2\pm 0.1)\)cm
Perimeter of a rectangle, p = 2(l + b)
= 2(10.5 + 5.2) = 31.4 cm
 \(\triangle p=\pm 2(\triangle l+\triangle b)\) 
\(=\pm 2(0.2+0.1)=\pm 0.6\)
Perimeter of a rectangle \(=(31.4\pm 0.6)\) 

Diameter of wire = (1.330 \(\pm \) 0.003) cm or D = 1.330 cm \(\pm \)0.3%.