A body cools from a temperature of \(3T\) to \(2T\) in \(10\) minutes. The room temperature is \(T.\) Assuming that Newton's law of cooling is applicable, the temperature of the body at the end of the next \(10\) minutes will be:
| 1. | \(\frac{7}{4}T\) | 2. | \(\frac{3}{2}T\) |
| 3. | \(\frac{4}{3}T\) | 4. | \(T\) |
| 1. | \(\dfrac{3}{2}R\) | 2. | \(\dfrac{5}{2}R\) |
| 3. | \(2R\) | 4. | \(R\) |
The temperature inside a refrigerator (reversible process) is t2oC and the room temperature is t1oC. The amount of heat delivered to the room for each joule of electrical energy consumed, ideally, will be:
1.
2.
3.
4.
A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?
| 1. | \(\dfrac{P}{kT}\) | 2. | \(\dfrac{Pm}{kT}\) |
| 3. | \(\dfrac{P}{kTV}\) | 4. | \(mkT\) |
A body of mass \(m\) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \(m\) is slightly pulled down and released, it oscillates with a time period of \(3~\text{s}\). When the mass \(m\) is increased by \(1~\text{kg}\), the time period of oscillations becomes \(5~\text{s}\). The value of \(m\) in \(\text{kg}\) is:
1. \(\dfrac{3}{4}\)
2. \(\dfrac{4}{3}\)
3. \(\dfrac{16}{9}\)
4. \(\dfrac{9}{16}\)
| 1. | \(L\) | 2. | \(2L\) |
| 3. | \(\dfrac{L}{2}\) | 4. | \(4L\) |
Three sound waves of equal amplitudes have frequencies of \((n-1),~n,\) and \((n+1).\) They superimpose to give beats. The number of beats produced per second will be:
| 1. | \(1\) | 2. | \(4\) |
| 3. | \(3\) | 4. | \(2\) |
| 1. | \(8~\text{mC}\) | 2. | \(2~\text{mC}\) |
| 3. | \(5~\text{mC}\) | 4. | \(7~\mu \text{C}\) |
A parallel-plate capacitor of area \(A\), plate separation \(d\) and capacitance \(C\) is filled with four dielectric materials having dielectric constants \(k_1, k_2,k_3\) and \(k_4\) as shown in the figure below. If a single dielectric material is to be used to have the same capacitance \(C\) in this capacitor, then its dielectric constant \(k\) is given by:
| 1. | \( {k}={k}_1+{k}_2+{k}_3+3 {k}_4\) |
| 2. | \({k}=\frac{2}{3}\left({k}_1+{k}_2+{k}_3\right)+2 {k}_4\) |
| 3. | \({k}=\frac{2}{3} {k}_4\left(\frac{{k}_1}{{k}_1+{K}_4}+\frac{{k}_2}{{k}_2+{k}_4}+\frac{{k}_3}{{k}_3+{k}_4}\right)\) |
| 4. | \(\frac{1}{{k}}=\frac{1}{{k}_1}+\frac{1}{{k}_2}+\frac{1}{{k}_3}+\frac{3}{2 {k}_4}\) |
The potential difference \(V_{A}-V_{B}\) between the points \({A}\) and \({B}\) in the given figure is:
| 1. | \(-3~\text{V}\) | 2. | \(+3~\text{V}\) |
| 3. | \(+6~\text{V}\) | 4. | \(+9~\text{V}\) |
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