A particle at rest on a frictionless table is acted upon by a horizontal force which is constant in magnitude and direction. A graph is plotted for the work done on the particle against the speed of the particle . If there are no frictional forces acting on the particle, the graph will look like:
1
Option a
2
Option b
3
Option c
4
Option d
Official Solution
Correct Option: (4)
Step 1: Apply the work–energy theorem. The work done by the force on the particle is equal to the change in kinetic energy:
Since the particle starts from rest,
Step 2: Express work as a function of velocity. This shows that work done varies as the square of the speed. Step 3: Analyse the nature of the graph. At ,
As increases, increases non-linearly
The curve is a parabola opening upward Step 4: Match with the given options. (a) Linear graph — incorrect
(b) Constant work — incorrect
(c) Saturating curve — incorrect
(d) Upward curving parabola — correctFinal Answer:
02
PYQ 2023
medium
physicsID: lpunest-
A motor drives a body along a straight line with a constant force.
The power developed by the motor must vary with time as:
1
Option a
2
Option b
3
Option c
4
Option d
Official Solution
Correct Option: (1)
Step 1: Use Newton’s second law. Since the force applied by the motor is constant:
Hence, the acceleration of the body is constant. Step 2: Write velocity as a function of time. For constant acceleration (starting from rest):
Thus, velocity increases linearly with time. Step 3: Write expression for power. Instantaneous power is given by:
Since is constant:
Step 4: Substitute . This shows:
So, power increases linearly with time, starting from zero. Step 5: Match with the given graphs. (a) Straight line through origin — Correct (b) Saturating curve — Incorrect
(c) Exponential-like curve — Incorrect
(d) Constant power — Incorrect Final Answer:
