Class 11th

This is a multiple choice answer as classified in NCERT Exemplar

(b) The sum of these numbers is 663.821. The number with least decimal places is 227.2 is correct to only one decimal places and the closest number to it 664.

This is a multiple choice answer as classified in NCERT Exemplar

(b) The zero after points are not significant. The number can be written as 0.069, Hence number of significant figure are four.

This is a short answer type question as classified in NCERT Exemplar

t₁=39.6s, t₂=39.9s and t₃=39.5s

Least count of measuring instrument =0.1s

Precision in the measurement =least count of the measuring instrument =0.1s

So mean value of 20 observation

Mean value of t= $\frac{t_1+t_2+t_3}{3}=\frac{39.6+39.9+39.5}{3}=39.7s$

Absolute error in

 t₁= t-t₁ = 39.7-39.6 =0.1s

In t₂= t-t₂ = 39.7-39.9=-0.2s

In t₃= t-t₁ = 39.7-39.5= 0.2s

Mean error = $\frac{0.1+0.2+0.2}{3}=0.17s\approx 0.2$

Accuracy in the measurement = $?0.2s$

This is a short answer type question as classified in NCERT Exemplar

For dimensional consistency LHS = RHS

[L]= [A]=L

As wt-kx should be dimensionless [wt]= [kx]=1

w [T]=k [L]=1

So w= [T]^-1 and k= [L]^-1

This is a short answer type question as classified in NCERT Exemplar

The formula for solid angle is

 solid angle = area/ (distance)²

= $\frac{1{cm}^2}{5{cm}^2}=\frac{1}{25}=4*{10}^{-2}steridian$

This is a short answer type question as classified in NCERT Exemplar

As we know, $\theta =\frac{l}{r}radian$

$\theta =\frac{\pi }{6}=\frac{l}{31}cm$

L=31 $*\frac{\pi }{6}cm=\frac{31*3.14}{6}cm=16.22cm$

Rounding off to three significant figures it would be 16.2cm

This is a short answer type question as classified in NCERT Exemplar

(a) Plane angle = l/r radian its si unit is radian but no dimension formula.

(b) Strain= $\frac{?L}{L}=\frac{changeinlength}{length}$ so no dimension

And g =9.8m/s²

(c) Gravitational constant G= 6.67 $*{10}^{-11}N{m}^2/{kg}^2$

(d) Reynold's number is a number having no dimension.

This is a short answer type question as classified in NCERT Exemplar

F= [MLT^-2]=100N…….1

Length L= 10m………….2

Time t= 100s……….3

Substituting the value of L and T  in eqn 1,2,3

M $*10*{100}^{-2}=100$

$\frac{M*10}{100*100}=100$

M=100 $*1000kg$

M= 10⁵kg

This is a short answer type question as classified in NCERT Exemplar

R_me= distance of moon from earth

R_se=distance of sun from earth

Let angle made by sun and moon is .

$\theta =\frac{A_{sun}}{R_{se}^2}=\frac{A_{moon}}{R_{me}^2}$

$\theta =\frac{\pi R_s^2}{R_{se}^2}=\frac{\pi R_m^2}{R_{me}^2}$

( $\frac{R_s}{R_{se}}$ )2 = ( $\frac{R_m}{R_{me}}$ )2

( $\frac{R_s}{R_m}$ )= ( $\frac{R_{se}}{R_{me}}$ )

Hence radius of sun and moon represents their sizes respectively.

This is a short answer type question as classified in NCERT Exemplar

It is given that 50 VSD $\approx 49\mathrm{M}\mathrm{S}\mathrm{D}$

1MSD = 50/49VSD

1VSD= 49/50MSD

Minimum inaccuracy = 1MSD-1VSD= 1MSD-49/50MSD=1/50 MSD

1MSD= 0.5mm

Minimum inaccuracy = 1/50 $*$ 0.5mm=0.01mm