Since time taken is same and W \(\frac { 2\pi }{ T } \)
Thus , \(\omega \)₁ : \(\omega \)₂= 1:1.

Node: It is a point on stationary wave at which amplitude of vibration of the particle is zero.
Antinode: It is a point on stationary wave at which amplitude of vibration of the particle is maximum.

\(\frac { 3{ k }_{ B }T }{ 2 } \)

(a) The surface tension is increased.
(b) The surface tension decreases.
(c) The angle of contact decreases.

When the monkey climbs up with uniform speed, then
T = mg = 40 kg x 10 ms^-2 = 400 N
The rope will not break.

Astronomy.

a = -10x follows the condition of SHM, acceleration\(\alpha \) -displacement hence, SHM.

Glass transmits about 50% of heat radiation coming from a hot source like the sun but does not allow the radiation from moderately hot bodies to pass through it. Due to this, when a car is left in the sun, heat radiation from the sun gets into the car but as the temperature inside the car is moderate, they do not pass back through its windows. Hence, inside of the car becomes considerably warmer.

Absolute pressur
\(p={ p }_{ a }+{ p }_{ g }\ \ [\because \ from\ Eq.(I)]\)
\(\\ =101\ kPa+199kPa=300kPa\)

Gravitational potential energy, i.e
\(U_{ h }=-\frac { GMm }{ R+h } =-\frac { gR^{ 2 }m }{ R+h } \left[ where,g=\frac { GM }{ R^{ 2 } } \right] \)
\(=-\frac { gR^{ 2 }m }{ R\left( 1+\frac { h }{ R } \right) } =-\frac { mgR }{ 1+\frac { h }{ R } } \)

(i)  The velocity of a body at any instant.
(ii) The acceleration  of the body and 
(iii) the net displacement of the body in a given time - interval. 

Given, time taken by light to reach the earth 
t = 3.0 billion yr
 \(=3\times { 10 }^{ 9 }yr\)
\(\\ =3\times { 10 }^{ 9 }\times 365\quad days\)
\(\\ =3\times { 10 }^{ 9 }\times 365\times 24\times 60\times 60s\)
\(\\ Speed\quad of\quad light(c)=3\times { 10 }^{ 8 }m/s\)
\(\\ \therefore Distance \ of \ the \ quasar \ from \ the \ earth\)
\(\\ D=c\times t\)
\(=(3\times { 10 }^{ 8 }\times 3\times { 10 }^{ 9 }\times 365\times 24\times 60\times 60)m\)
\(=2.84\times { 10 }^{ 25 }m\quad =\quad 2.84\times { 10 }^{ 22 }km \) 

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