MCQ
Star $A$ has radius $ r$ surface temperature $T$ while star $B$ has radius $4r$ and surface temperature $T/2$ . The ratio of the power of two starts, $P_A : P_B$ is
- A$16:1$
- B$1:16$
- ✓$1:1$
- D$1:4$
✓
Answer
Correct option: C.
$1:1$
c
(c) Power $P \propto A{T^4} \propto {r^2}{T^4}$
(c) Power $P \propto A{T^4} \propto {r^2}{T^4}$
==> $\frac{{{P_2}}}{{{P_1}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} \times {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^4}$$ = {\left( {\frac{{4r}}{r}} \right)^2} \times {\left( {\frac{{T/2}}{T}} \right)^4}$ $=1$ .
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A body of mass $5 \,kg$ is moving with a momentum of $10\, kg-m/s$. A force of $0.2 \,N$ acts on it in the direction of motion of the body for $10\, seconds$. The increase in its kinetic energy is ............... $J$
→In case of displacement method of lenses, the product of magnification in both cases is
In $L-C-R$ circuit $V$ , $V_R$ , $V_L$ , $V_C$ are voltage of source, resistance, inductance and capacitor at any instant then choose the correct relation
→The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ......... $\%$
→Refer to the graph in figure. Match the following
Maximum number of beats frequency heard by a human being is
A force $\vec F\, = \,(2\hat i\, - \,\hat j\, + 3\hat k)$ is acting at a point $(-1, 2, -3).$ Find its torque about the origin
→$n$ drops of $a$ liquid, each with surface energy $E$, joining to form a single drop
→A convex mirror of focal length $10\,cm$ is shown in figure. A linear object $AB = 5\,cm$ is placed along the optical axis. Point $B$ is at distance $20\,cm$ from the pole of mirror. Then size of image of $AB$ will be
→A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is
→