Potential energy, spring energy and conservative forces — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The elastic potential energy stored in an ideal spring stretched by x is

• A. $U=\frac12kx^2$
• B. $U=kx$
• C. $U=\frac12kx$
• D. $U=k/x$

Question 2 · difficulty L2 · understanding

A force is conservative if the work done between two points

• A. is independent of path
• B. always equals zero
• C. depends only on speed
• D. depends on time taken

Question 3 · difficulty L2 · understanding

For a conservative force, work done by the force is related to potential-energy change by

• A. $W=-\Delta U$
• B. $W=\Delta U$
• C. $W=U_i+U_f$
• D. $W=0$ always

Question 4 · difficulty L2 · understanding

Which force is commonly treated as conservative?

• A. Gravitational force
• B. Kinetic friction
• C. Viscous drag
• D. Air resistance

Question 5 · difficulty L3 · application

A spring of constant 200 N/m is stretched by 0.10 m. How much elastic potential energy is stored?

• A. 1.0 J
• B. 2.0 J
• C. 10 J
• D. 20 J

Question 6 · difficulty L3 · application

If a spring extension is doubled, its elastic potential energy becomes

• A. four times
• B. twice
• C. half
• D. unchanged

Question 7 · difficulty L3 · application

A conservative force does 30 J of positive work on a particle. The potential energy changes by

• A. -30 J
• B. +30 J
• C. 0
• D. +60 J

Question 8 · difficulty L3 · application

A particle moves from point A to B under gravity alone along two different paths. The gravitational work done is

• A. the same for both paths
• B. larger for the longer path
• C. smaller for the curved path
• D. zero for both paths always

Question 9 · difficulty L4 · application

A spring is compressed from x = 0 to x = a. How much work must an external agent do quasistatically?

• A. $\frac12ka^2$
• B. $ka^2$
• C. $ka$
• D. $0$

Question 10 · difficulty L4 · application

The potential energy of a one-dimensional system is $U(x)=2x^2$ J. What is the force at x = 3 m?

• A. -12 N
• B. +12 N
• C. -6 N
• D. +6 N