Forces

Let the magnitudes of the two forces be and , where and (since their magnitudes are in the ratio 5:3). The resultant of the two forces is given by the formula: where is the angle between the two forces. Substituting the known values: Simplify: Now, substitute into the expressions for and : Thus, the magnitudes of the two forces are and . The correct answer is option (3), and .

Step 1: Using Newton's Second Law of Motion.
The force required to change the velocity of an object is: where: \begin{itemize} \item , \item (deceleration). \end{itemize}
Step 2: Calculate the force.
Using , we get: The magnitude of the force is , which is the required force to stop the body.

The horizontal direction is usually represented by the x-axis.
So, we need to find the angle that the force vector makes with the unit vector along the x-axis, which is .
The magnitude of the force vector is: $ and the unit vector along the horizontal is: \) and is also given by , where is the angle between them.
In our case, and .
The magnitude of is .
\) is: \) $

Mass of coal kg.
Depth (height) m.
Time taken hour seconds.
Acceleration due to gravity .
Work done in lifting the coal (Output Work) = Potential energy gained by coal.
Joules.
Output Power .
Watts.
kW.
Efficiency .
Given efficiency .
The "power of the crane" usually refers to its input power .
This matches option (4).

The work done by the motor is equal to the potential energy required to lift the water: where , , and . The power is the work done per unit time: Using the efficiency of the pump, the actual power is:

Step 1: Initially, both masses are at rest, so the total momentum of the system is zero. Step 2: Since no external force is acting on the system, the velocity of the center of mass (CM) remains constant. Step 3: If it starts from rest, the center of mass continues to be at rest. Hence, regardless of the motion of the individual particles due to internal forces (mutual attraction), the center of mass velocity remains: % Final Answer

Step 1: Understanding Power in Motion The instantaneous power is given by: Since the body moves at a uniform speed, the net force acting on it is responsible for the power generation. Step 2: Net Force on the Body The forces and act in opposite directions. The net force exerted on the body is: Step 3: Computing Net Power Multiplying the net force by velocity: Thus, the correct answer is:

Step 1: Understanding Power in Motion The instantaneous power is given by: Since the body moves at a uniform speed, the net force acting on it is responsible for the power generation. Step 2: Net Force on the Body The forces and act in opposite directions. The net force exerted on the body is: Step 3: Computing Net Power Multiplying the net force by velocity: Thus, the correct answer is:

Step 1: Calculate the work done on the ball
Mass kg, final speed m/s, initial speed , distance m. Kinetic energy gained by the ball = J. Work done , so , N. Step 2: Alternative approach using kinematics
Use : , , m/s . Net force N. Step 3: Match with options
The net force 20 N matches option (2).