You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Physics

Conduction

Four spheres ...

Question

Four spheres $A, B, C$ and $D$ of different metals but of same radius are kept at same temperature. The ratio of their densities is $2 : 3 : 5 : 1$ . If specific heats of their materials are in the ratio $3 : 6 : 2 : 4$ , which sphere will show initially the fastest rate of cooling?

D

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $B$
Rate of loss of heat: $\frac{d Q}{d t} = m s \frac{d T}{d t}$
RHS has product of mass and specific heat. This is max for sphere $B$ ( $3$ $\times$ $6$ )
Hence, sphere $B$ has fastest rate of cooling.

Suggest Corrections

Similar questions

Q. Four spheres

A, B, C

and

D

of different metals but of same radius are kept at same temperature.The ratios of their densities and specific heats are

2 : 3 : 5 : 1

and

3 : 6 : 2 : 4 .

Which sphere will show the fastest rate of cooling (initially)?

Two spheres of same radius $R$ have their densities in the ratio $8 : 1$ and the ratio of their specific heats are $1 : 4$ . If by radiation their rates of fall of temperature are same, then find the ratio of their rates of losing heat.

Q. Two spheres have their radii in the ratio 1 : 2, the densities of their materials are in the ratio 2 : 3 and their specific heats are in the ratio 3:4, then the ratio of their thermal capacities is

Q. A solid sphere of radius

4 cm

and a hollow sphere of same material and having outer radius

4 cm

and inner radius

2 cm

are heated to the same temperature and allowed to cool in the same room. The ratio of the rate of fall of temperatures is

Q. Two spheres of radii

R_{1}

and

R_{2}

have densities

ρ_{1}

and

ρ_{2}

and specific heat

C_{1}

and

C_{2}

. If they are heated to the same temperature, the ratio of their rates of cooling will be

Join BYJU'S Learning Program

Four spheres A,B,C and D of different metals but of same radius are kept at same temperature. The ratio of their densities is 2:3:5:1. If specific heats of their materials are in the ratio 3:6:2:4, which sphere will show initially the fastest rate of cooling?

The correct option is C BRate of loss of heat: dQdt=msdTdtRHS has product of mass and specific heat. This is max for sphere B ( 3 × 6 )Hence, sphere B has fastest rate of cooling.

Four spheres $A, B, C$ and $D$ of different metals but of same radius are kept at same temperature. The ratio of their densities is $2 : 3 : 5 : 1$ . If specific heats of their materials are in the ratio $3 : 6 : 2 : 4$ , which sphere will show initially the fastest rate of cooling?

The correct option is C $B$
Rate of loss of heat: $\frac{d Q}{d t} = m s \frac{d T}{d t}$
RHS has product of mass and specific heat. This is max for sphere $B$ ( $3$ $\times$ $6$ )
Hence, sphere $B$ has fastest rate of cooling.