Question Discussion & Solution

Hence, “21” will come next.

CONCEPT:

Equilibrium of a rigid body:

• A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
• Condition for the mechanical equilibrium:
  1. The total force, i.e. the vector sum of the forces, on the rigid body is zero.
  2. The total torque, i.e. the vector sum of the torques on the rigid body is zero.

⇒ \(\rm\vec{F_1}+\vec{F_2}+...+\vec{F_n}=0\)

⇒ \(\rm \vec{τ_1}+\vec{τ_2}+...+\vec{τ_n}=0\)

• If the forces on a rigid body are acting in the 3 dimensions, then six independent conditions to be satisfied for the mechanical equilibrium of a rigid body.
• If all the forces acting on the body are coplanar, then we need only three conditions to be satisfied for mechanical equilibrium.
• A body may be in partial equilibrium, i.e., it may be in translational equilibrium and not in rotational equilibrium, or it may be in rotational equilibrium and not in translational equilibrium.

EXPLANATION:

• A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
• We know that the linear acceleration and the angular acceleration of a stationary body are zero.

A book is kept on a table:

• In this case, the book will be stationary so it is an example of the equilibrium of a body.

A ball is moving downward freely under gravity:

• We know that when a ball moves freely under gravity, then only the gravitational force will act on the ball due to which the ball accelerates downward.
• Therefore ball is moving downward freely under gravity is not an example of the equilibrium of a body.
• Hence, option 1 is correct.

The pattern followed is:

There are two series here:

i) 5, 10, 20, 40, 80

5 × 2 = 10

10 × 2 = 20

20 × 2 = 40

40 × 2 = 80

ii) S, R, Q, P, O

S - 1 = R

R - 1 = Q

Q - 1 = P

P - 1 = O

Hence, the correct answer is "80O".

The correct answer is In 1240.

• Razia Sultan was removed from the throne in1240.

Key Points

• Razia Sultan (1236 AD-1240 AD):
  • She belonged to the Slave Dynasty.
  • She was the first and last Muslim woman ruler of Medieval India.
  • She appointed Jamaluddin Yakoot as the highest officer of cavalry.
  • She abandoned Pardah and appeared before the public in male dress.
  • She saved the empire from Mongol invasion.
  • She died in the year 1240 AD.

For this question,

Statements: The money plant has thin leaves and requires more water.

This statement explains the requirements and speciality of the Money plant.

Conclusion I: Plants with thin leaves require more water..

It can not be true as the statement is all about the Money plants but except for money plants, there are more plants that have thin leaves.

Conclusion II: Money plants cannot be grown in places with water scarcity.

It is completely according to the statement as it is true.

Hence, Option (4) is correct.

Additional Information

• If there are two or more sentences that are used to frame a statement, then, the sentences must be interrelated, and mutual contradiction should be there.
• Do not look for truthful notions. The information provided in the statement is the only requirement for a student to answer the question. No assumptions must be made.
• Read the statement carefully and look for keywords that are common between the statement and the conclusions
• If there is more than one conclusion that is applicable to the statement, students must ensure that the conclusions they opt for have some relation with each other.