Test: Work and Energy- Assertion & Reason Type Questions- 1 - Class 9 MCQ

Assertion (A) is true but reason (R) is false.  (A).

Work done by a force is given by the equation: W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors. The angle between the force and displacement vectors is measured in radians. The cosine of the angle is positive when the force and displacement vectors are in the same direction, and negative when they are in opposite directions. The work done by the force can be positive or negative depending on the direction of the force and displacement. If the force and displacement are in the same direction, the work done is positive and if they are in opposite direction, the work done is negative. The reason given in the statement that force is taken as positive when it acts opposite to the direction of displacement, supports the assertion that work done by the force can be positive or negative.

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

The work done by a force on an object is given by the equation W = F * d * cos(θ), where F is the force, d is the displacement and θ is the angle between the force and displacement vectors. In this case, the girl is running along a circular path with a uniform speed. The force acting on her is the force of gravity, which is always perpendicular to the surface of the earth. The angle between the force and displacement vectors is 90 degrees, so cos(90) = 0.

Since the angle between the force and displacement vectors is 90 degrees, the work done by the force of gravity on the girl is zero. Additionally, the reason given in the statement that displacement is zero after one complete rotation, also supports the assertion that the work done by the girl is zero.

P = 1000/10 = 100W

SI unit of power is Watt. One kWh is equal to 3.6 ×10⁶ J.

For crane P: The work done by the crane P is equal to W_P = mgh. The power supplied by the crane will be P_P = W_P/t = mgh/1 = mgh and the fuel consumed will also be the same.

For crane Q: The work done by the crane Q is equal to W_Q = mgh. The power supplied by the crane will be P_Q = W_Q/t = mgh/2 and the fuel consumed will also be the same.

As you can see that P_Q = P_P/2 → P_P = 2P_Q, which means that the crane P consumes two times more fuel than crane Q and also crane P supplies two times more power than crane Q.