Question Discussion & Solution

Concept:

• Potential Energy: The energy of an object obtained by doing work against the conservative forces like spring force and gravitational force is called potential energy.
• The Gravitational potential energy of an object at a height h from the ground is given as

P = mgh

The spring potential energy of spring when it is stretched x distance from its natural length is given as

 \(P = \frac{1}{2}kx^2\)

• Kinetic Energy: The energy obtained by an object by virtue of its motion is called kinetic energy.

\(K = \frac{1}{2}mv^2\)

K is kinetic energy, v is the speed of the object, m is the mass of the object.

• Mechanical Energy: The sum of potential energy and kinetic energy is called mechanical energy.

Explanation:

So, from the above concept, it is clear that total mechanical energy is the sum of potential energy and kinetic energy. 

So, the answer is the Sum of Kinetic Energy and Potential Energy.

Key PointsBiogas:

• Biogas is an emerging renewable, non-conventional energy source that is obtained through the degradation of organic matter by bacteria under anaerobic conditions.
• The major constituent of biogas is Methane.
• Biogas is usually made up of around 50-70% methane (CH4) and 25-45% carbon dioxide (CO2), with other gases such as hydrogen (H2), hydrogen sulphide (H2S), watervapour (H2O), Nitrogen (N2), oxygen (O2), ammonia (NH3) making up the rest.
• It is released when Cow, Buffalo, and Pig manure is processed anaerobically i.e. in the absence of Oxygen.
• Biogas can be used for Space Heating, Generation of Electricity, Fuel for Cooking, etc.

Important Points

Advantages of Biogas - 

• ​Biogas burns without smoke; hence no harmful gas such as CO₂, CO, NO₂, and SO₂ are evolved.
• The slurry produced after the production of biogas is used as manure in fields.
• The method of disposal is safe and efficient and hence no space is wasted in the form of landfills.
• Biogas plants require very little installation costs and become self-sufficient in a span of 3-4 months.
• Work opportunity for thousands of people is created, especially in rural areas.

Thus, Biogas is a non-conventional type of natural resource.

Additional Information

There are basically two sources of energy:

The mirror image of this image is:

Hence, option (2) is the correct answer.

The correct answer is Karauli.

• The princely state of Karauli was founded by the Yaduvanshi ruler Arjun Singh under the name Kalyanpuri in Vikram Samvat 1405 (1348 AD), which later became Karauli in the period.

Key Points

• The ruler of Karauli, Harvakshpal Singh, made a treaty with the British.
• Karauli was the first princely state of Rajasthan, which made the first treaty with the British.
• Anjani Mata is the local deity of the princely state of Karauli.

Additional Information

• Karauli State was a princely state in India.
  • It existed from 1348 to 1949.
  • It is located in the Braj region.
  • Its capital was Karauli city.
• The important towns associated were Mandrayal or Mandrail.
• The 32nd district of Karauli Rajasthan was created on 19 July 1997, separated from Sawai Madhopur.
• Ramgopal Vijayvargiya was a well-known painter from Karauli, who started the solo painting exhibition tradition.

Important Points

• Lootmar Holi / Lathmar Holi of Mahavir Ji (Karauli) is very famous.
• Shivaratri Cattle Fair - This fair starts on Phalgun Krishna Trayodashi.
  • This fair is famous for the purchase and sale of cows of the Haryanvi breed.

The correct answer is 4°C.

• Freezing of Water:
  • As water freezes, cold water (or ice formed) comes on the surface and warm water goes down.
  • Since the freezing temperature of the water is 0ºC or 273 K.
  • So water at the bottom should be at a higher temperature.
  • Water density at 4ºC is more than the density of water at 0ºC, hence the correct option is 4ºC.

​Key Points

• Reason of low temperature at bottom of the top layer:
  • This is due to the process of convection.
  • When the temperature of the water at the top layer reaches the freezing point, it is converted to ice.
  • But ice is lighter than water, so it will not sink to the bottom.
  • So there will be ice on the top surface and water would remain at the bottom of the lake.