How many seconds does it take a metal ball to drop 200. m from rest?

1) 6.39 s

2) 4.28 s

3) 8.58 s

4) 7.29 s

1) 6.39 s

2) 4.28 s

3) 8.58 s

4) 7.29 s

Correct Answer :1

A ball is dropped from rest. What is its speed after 3 seconds?

(1) 15 m/s

(2) 25 m/s

(3) 30 m/s

(4) 45 m/s

(1) 15 m/s

(2) 25 m/s

(3) 30 m/s

(4) 45 m/s

Correct Answer :3

A vessel of volume 0.2m^{3} contains hydrogen gas at temperature 300K and pressure 1bar1bar. Find the heat (in kcal) required to raise the temperature to 400K. The molar heat capacity of hydrogen at constant volume is (5 cal/molK)

1) 4

2) 2

3) 1

4) 8

Correct Answer :1

Volume of hydrogen: $$V= 0.2 m^3 = 0.2 \times 10^6 \:cm^3$$

No of moles of hydrogen: $$n =0.987\times \dfrac{ 0.2 \times 10^6}{22.4 \times 10^3}$$ since $$1\:m^3 = 10^6\:cm^3$$

Heat required to raise the temp of hydrogen from $$300K$$ to $$400K$$: $$Q= nC\Delta T=0.987\times \dfrac{ 0.2 \times 10^6}{22.4 \times 10^3} \times 5 \times (400-300)=4.01\:kcal$$

Emission of energy from sun is :

(1) by chemical reactions

(2) by radio activity

(3) by fusion

(4) by fission

Correct Answer :3

Two loops of different wire are placed concentrically in a plane. If the current in the outer loop is made to pass clock wise and current increases with time, the induced current in the inner loop will be :

(1) will depend upon radius of loop.

(2) zero

(3) anticlock wise

(4) clock wise

Correct Answer :3

The activity of a radioactive sample can be increased by:

(1) applying intense electric field

(2) no method

(3) heating it.

(4) applying pressure on it.

(1) applying intense electric field

(2) no method

(3) heating it.

(4) applying pressure on it.

Correct Answer :2

A worker does 500 J of work on a 10 kg box. If the box transfers 375 J of heat to the floor through the friction between the box and the floor, what is the velocity of the box after the work has been done on it?

1) 5 m/s

2) 10 m/s.

3) 12.5 m/s

4) 50 m/s

Correct Answer :1

Given : $$m = 10$$ kg

Frictional force does negative work i.e $$W_f = -375$$ J

Work done by worker $$W = 500$$ J

Using work-energy theorem : $$W_{all force} = \Delta K.E$$

$$\therefore$$ $$W + W_f = \dfrac{1}{2}mv^2 - \dfrac{1}{2}mu^2$$

OR $$500 - 375 = \dfrac{1}{2}\times 10v^2 - 0$$ $$(\because u = 0 m/s)$$

$$\implies v = \sqrt{25} = 5$$ m/s

The charge flowing through a resistance $$R$$ varies with time $$t$$ as $$Q=at-b{t}^{2}$$. The total heat produced in $$R$$ by the time current ceases is

1) $${a}^{3}R/6b$$

2) $${a}^{3}R/3b$$

3) $$\cfrac{{a}^{3}R}{2b}$$

4) $$\cfrac{{a}^{3}R}{b}$$

Correct Answer :1

Given,

$$Q= at- bt^{2}$$

$$i=\cfrac{dQ}{dt}=\cfrac{d}{dt} \cdot (at-bt^{2})$$

$$\Rightarrow i= \cfrac{d}{dt} \cdot at -\cfrac{d}{dt} \cdot bt^{2}$$

$$\Rightarrow i= a\cdot \cfrac{d}{dt} - b\cdot \cfrac{d}{dt}t^{2}$$

$$\Rightarrow i= a- 2bt$$

we know, $$H=\int { { i }^{ 2 }\cdot } Rdt$$

Now, for the limits of integration,

when $$i=0, \quad a=2bt$$

$$\therefore t=\cfrac { a }{ 2b } $$

$$H= \int _{ a }^{ a/2b}{ { { i }^{ 2 }\cdot }Rdt }$$

$$\Rightarrow H=\int _{ a }^{a/2b} \left( { a }^{ 2 }+4{ b }^{ 2 }t^{ 2 }-\quad 4bt \right) Rdt=\quad R\left[ { a }^{ 2 }t+\cfrac { 4{ b }^{ 2 }t^{ 3 } }{ 3 } -\cfrac { 4ab{ t }^{ 2 } }{ 2 } \right] _{ 0 }^{ a/2b }$$

$$\Rightarrow H=R\left[ { a }^{ 2 }\left( \cfrac { a }{ 2b } \right) +\cfrac { 4{ b }^{ 2 } }{ 3 } \left( \cfrac { { a }^{ 3 } }{ 8{ b }^{ 3 } } \right) -\cfrac { 4ab }{ 2 } \left( \cfrac { { a }^{ 2 } }{ 4{ b }^{ 2 } } \right) \right] =\quad R\left[ \cfrac { { a }^{ 3 } }{ 2b } +\cfrac { { a }^{ 3 }{ b }^{ 3 } }{ 6{ b }^{ 3 } } -\cfrac { { a }^{ 3 } }{ 6b } \right] =\quad R\left[ \cfrac { 3{ a }^{ 3 }{ b }^{ 3 }+\quad { a }^{ 3 }{ b }^{ 2 }-{ 3a }^{ 3 }{ b }^{ 3 } }{ 6{ b }^{ 3 } } \right] $$

$$\Rightarrow H=\quad R\left[ \cfrac { { a }^{ 3 } }{ 6b } \right] =\quad \cfrac { R{ a }^{ 3 } }{ 6b } $$

When a ray of light enters a glass slab from air

1. Its wavelength increase

2. No change in frequency & wavelength

3. Its frequency increases

4. No change in frequency & wavelength

1. Its wavelength increase

2. No change in frequency & wavelength

3. Its frequency increases

4. No change in frequency & wavelength

Correct Answer :2

The wavelength of light ray decreases as it enters a glass slab from air.