Two planets move around the sun. The periodic times and the mean radii of the orbits are $T_{1}, T_{2} a n d r_{1}, r_{2}$ respectively. The ratio $\frac{T_{1}}{T_{2}}$ is equal to

Q. The radioactivity of a sample is

R_{1}

at time

T_{1}

and

R_{2}

at time

T_{2}

. If the half life of the specimen is

T

, number of atoms that have disintegrated in time

(T_{2} - T_{1})

is proportional to

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Two spherical black bodies have radii ′r′1 and ′r′2. Their surface temperatures are ′T′1 and ′T′2. If they radiate same power then r2r1 is

The correct option is B (T1T2)2P1=AσT41=πr21σT41P2=AσT42=πr22σT42P1=P2so r2r1=T21T22

Two spherical black bodies have radii $^{'} r_{1}^{'}$ and $^{'} r_{2}^{'}$ . Their surface temperatures are $^{'} T_{1}^{'}$ and $^{'} T_{2}^{'}$ . If they radiate same power then $\frac{r_{2}}{r_{1}}$ is

The correct option is B ${(\frac{T_{1}}{T_{2}})}^{2}$
$P_{1} = A σ T_{1}^{4} = π r_{1}^{2} σ T_{1}^{4}$
$P_{2} = A σ T_{2}^{4} = π r_{2}^{2} σ T_{2}^{4}$
$P_{1} = P_{2}$
so $\frac{r_{2}}{r_{1}} = \frac{T_{1}^{2}}{T_{2}^{2}}$