Kinematics

Step 1: Stefan-Boltzmann Law.
According to the Stefan-Boltzmann law, the power radiated by a black body is proportional to the fourth power of its temperature: where is the power, is the Stefan-Boltzmann constant, is the surface area, and is the temperature of the body.
Step 2: Surface area of spherical bodies.
The surface area of a sphere is , where is the radius of the sphere.
Step 3: Equating power radiated.
For both bodies to radiate the same power: Simplifying, we get:
Step 4: Conclusion.
The ratio is: Hence, the correct answer is (A).

Step 1: Understanding the motion of clock hands.
The hour hand makes one full rotation (i.e., radians) in 12 hours, and the second hand makes one full rotation (i.e., radians) every 60 seconds. - Angular speed of hour hand: - Angular speed of second hand: Step 2: Calculating the relative angular speed.
The relative angular speed is the difference between the angular speeds of the second hand and the hour hand: Simplifying this: Thus, the correct answer is (B) .

Concept: For motion under gravity with constant acceleration, we use the kinematic equation: where
• = initial velocity
• = final velocity
• = acceleration due to gravity
• = height fallen

Step 1: Identify the given quantities. Since the stone is dropped:

Step 2: Substitute into the kinematic equation.

Step 3: Find the velocity. Thus the velocity just before hitting the ground is

Concept: For motion under constant acceleration, we use the kinematic equation where = initial velocity, = final velocity, = acceleration due to gravity, = maximum height. At the highest point, the velocity becomes zero.

Step 1: Substitute the given values. Initial velocity: At maximum height: Using

Step 2: Solve for . Thus, the maximum height reached is metres.