Q: For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

We know that, Potential energy, \$U=-\dfrac{G{{M}_{e}}m}{{{R}_{e}}}\$ Where, \${{M}_{e}}=\$Mass of the earth \$m=\$Mass of satellite \${{R}_{e}}=\$ Radius of the earth \$G=\$ Gravitational constant Now, \$|U|=\dfrac{G{{M}_{e}}m}{{{R}_{e}}}\$ Now, kinetic energy \$K=\dfrac{1}{2}\dfrac{G{{M}_{e}}m}{{{R}_{e}}}\$ Now, \$ \dfrac{K}{|U|}=\dfrac{1}{2}\dfrac{G{{M}_{e}}m}{{{R}_{e}}}\times \dfrac{{{R}_{e}}}{G{{M}_{e}}m} \$ \$ \dfrac{K}{|U|}=\dfrac{1}{2} \$ Hence, the ratio of kinetic energy to potential energy is \$\dfrac{1}{2}\$

Question 1

An object is placed at a distance of 10 cm from a concave mirror of focal length 20 cm.a) Draw ray diagram for the formation of image b) Calculate the image distancec) state 2 characteristics of the image formed.

Accepted Answer

Given: Focal length of concave mirror, f = -20 cmDistance of object from the mirror, u = -10 cmuse formula, 1/v + 1/u = 1/f or, 1/v = 1/f - 1/u or, 1/v = 1/-20 - 1/-10 or, 1/v = -1/20 + 1/10 = 1/20 or, v = +20cm hence, image position is the 20cm right side from the pole of the concave mirror as shown in the diagram. The image is straight and bigger than the object.

Question 2

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

Accepted Answer

We know that,&#10;&#10;Potential energy,&#10;&#10;$U=-\dfrac{G{{M}_{e}}m}{{{R}_{e}}}$ &#10;&#10;Where,&#10;&#10;${{M}_{e}}=$Mass of the earth&#10;&#10;$m=$Mass of satellite &#10;&#10;${{R}_{e}}=$ Radius of the earth&#10;&#10;$G=$ Gravitational constant&#10;&#10;Now,&#10;&#10;$|U|=\dfrac{G{{M}_{e}}m}{{{R}_{e}}}$ &#10;&#10;Now, kinetic energy&#10;&#10;$K=\dfrac{1}{2}\dfrac{G{{M}_{e}}m}{{{R}_{e}}}$  &#10;&#10;Now, &#10;&#10;  $ \dfrac{K}{|U|}=\dfrac{1}{2}\dfrac{G{{M}_{e}}m}{{{R}_{e}}}\times&#10;\dfrac{{{R}_{e}}}{G{{M}_{e}}m} $ &#10;&#10; $ \dfrac{K}{|U|}=\dfrac{1}{2}&#10;$ &#10;&#10;Hence, the ratio of kinetic energy to potential energy&#10;is $\dfrac{1}{2}$

Question 3

Two charges of $1.0\ C$ each are placed one meter apart in free space. The force between them will be

Accepted Answer

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Question 4

The Young's modulus for perfectly rigid body is _______.

Accepted Answer

For a perfectly rigid body, strain is always zero, for all values of stress. So, its Young's Modulus would be infinity.

Question 5

Which of the following is not due to total internal reflection?

Accepted Answer

Correct Answer: Option CExplanation of Correct Answer: The apparent depth of a pond seems to be less than the real&#10;depth is due to the phenomenon of refraction of light and not due to total&#10;internal reflection. Whereas formation of mirage on hot summer days, the brilliance&#10;of diamond and working of optical fiber are based on total internal reflection.&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;So, the difference between the apparent and real depth of a pond&#10;is the answer.

Question 6

Permanent hardness of water is due to the presence of ___________.

Accepted Answer

Permanent hardness in water is due to the presence of the chlorides, nitrates and sulphates of calcium and magnesium. It is not precipitated by boiling. These minerals in water can cause some everyday problems. Hard water may also shorten the life of plumbing and water heaters. The lime scale can build up on the inside of the pipe restricting the flow of water or causing a blockage.

Question 7

For a particle having a uniform circular motion, which of the following constant?

Accepted Answer

In a uniform circular motion speed is constant. Other are vector quality that is changing.

Question 8

Which one of the following is not a part of female reproductive system?

Accepted Answer

The female reproductive system is made up of the internal and external sex organs that function in reproduction. The internal sex organs are the uterus and Fallopian tubes, and the ovaries. The vagina which is an external organ is connected to the uterus at the cervix. The urethra is not a reproductive organ. It is the tube that carries urine from the bladder to outside of the body.

Question 9

Biodiversity refers to the number and variety of organisms found within a particular habitat. Which of the following is one of the measures of biodiversity?

Accepted Answer

Biodiversity is a term that is used to refer to the crowd of living organisms that occupy the variety of habitats on the earth and have adapted to suit their lives according to the environment they inhabit. The biodiversity can be studied at the following three levels: GENETIC BIODIVERSITY: This refers to the genetic variation within the same species, for example, the colour of fur in cats. SPECIES BIODIVERSITY: This refers to the variety of species occupying a particular area. A species can be defined as the group of organisms that are capable of interbreeding.ECOSYSTEM BIODIVERSITY: This refers to the biodiversity present in the different ecosystem, for example, tropics have a higher degree of biological diversity as compared to temperate or polar regions.

Question 10

The relation between coefficient of linear expansion and coefficient of volume expansion is

Accepted Answer

Relation between coefficient of linear expansion and coefficient of real expansion:Consider a thin rectangular parallelopiped solid of length, breadth, height and volume $l_o&#8203;\ b_o&#8203;\ h_o&#8203;\ V_o&#8203;$ at temperature $0^{o}C$. Let the solid be heated at some higher temperature say to C.Let $l,b,h,V$ be the length, breadth, height and volume at temperature to C.Then the original volume $V_o&#8203;=l_o&#8203;b_o&#8203;h_o&#8203;$ ....(1)Consider linear expansionlength $l=l_o&#8203;(1+\alpha t)$breadth $b=b_o&#8203;(1+\alpha t)$height $h=h_o&#8203;(1+\alpha t)$where $\alpha =coefficient \ of \ linear\  expansion$Final volume $V=lbh=l_o&#8203;(1+ \alpha t)&#215;b_o&#8203;(1+ \alpha t)&#215;h_o&#8203;(1+\alpha t)$$V=l_ob_oh_o(1+3 \alpha t+3  \alpha^2t^2+ \alpha^3t^3)$\alphaNow, $ \alpha $ is very small hence $ \alpha^2$ is still small, hence quantity $ \alpha^2t^2\  \alpha^3t^3$ can be neglected.$V=V_o&#8203;(1+3\alpha t)$ .....(2)Considering cubical expansion of the solid$V=V_o&#8203;(1+\gamma t)$From (1) and (2),$\gamma=3\alpha$