Free Trail Quiz | Hard Questions

📖 Physics 🔴 Hard

Q1. A particle moves under a force \(F=-kx+\alpha x^3\), where \(k,\alpha>0\). The potential energy function taking \(U(0)=0\) is

A. \(\frac{kx^2}{2}-\frac{\alpha x^4}{4}\)

B. \(-\frac{kx^2}{2}+\frac{\alpha x^4}{4}\)

C. \(\frac{kx^2}{2}+\frac{\alpha x^4}{4}\)

D. \(-\frac{kx^2}{2}-\frac{\alpha x^4}{4}\)

📖 Physics 🔴 Hard

Q2. A particle moves in circular orbit under central force \(F=-kr^3\). Total energy of orbit radius \(R\) equals

A. \(-\frac{kR^4}{4}\)

B. \(-\frac{kR^4}{2}\)

C. \(\frac{kR^4}{4}\)

D. \(0\)

📖 Physics 🔴 Hard

Q3. A particle moves in one dimension under potential energy \(U=ax^2-bx\). Position of stable equilibrium is

A. \(\dfrac{b}{2a}\)

B. \(\dfrac{a}{2b}\)

C. \(\dfrac{b}{a}\)

D. \(\dfrac{2b}{a}\)

📖 Physics 🔴 Hard

Q4. A force varies as \(F=F_0e^{-x/L}\). Work done from \(x=0\) to \(x=L\ln3\) is

A. \(\frac{2F_0L}{3}\)

B. \(\frac{F_0L}{2}\)

C. \(F_0L\)

D. \(\frac{F_0L}{3}\)

📖 Physics 🔴 Hard

Q5. A block slides from top of smooth sphere radius \(R\). Speed when it leaves sphere is

A. \(\sqrt{\frac{2gR}{3}}\)

B. \(\sqrt{gR}\)

C. \(\sqrt{2gR}\)

D. \(\sqrt{\frac{4gR}{3}}\)

📖 Physics 🔴 Hard

Q6. A block of mass \(m\) is projected up a rough inclined plane of angle \(\theta\) with initial speed \(u\). Coefficient of friction is \(\mu\). The distance travelled before coming to rest is

A. \(\dfrac{u^2}{2g(\sin\theta+\mu\cos\theta)}\)

B. \(\dfrac{u^2}{2g(\sin\theta-\mu\cos\theta)}\)

C. \(\dfrac{u^2}{g(\sin\theta+\mu\cos\theta)}\)

D. \(\dfrac{u^2}{2g\sin\theta}\)

📖 Physics 🔴 Hard

Q7. A body of mass \(m\) moving with speed \(u\) collides elastically with another body of mass \(m\) at rest. Fraction of initial kinetic energy retained by first body after collision is

A. \(0\)

B. \(\frac12\)

C. \(1\)

D. \(\frac14\)

📖 Physics 🔴 Hard

Q8. A body projected from ground with speed \(u\) at angle \(\theta\). Potential energy at maximum height is

A. \(\dfrac{mu^2\sin^2\theta}{2}\)

B. \(mu^2\sin^2\theta\)

C. \(\dfrac{mu^2}{2}\)

D. \(mgh\)

📖 Physics 🔴 Hard

Q9. A particle moves with speed \(v\) under force \(F\). If power is constant, acceleration varies as

A. \(\dfrac1v\)

B. \(v\)

C. \(v^2\)

D. constant

📖 Physics 🔴 Hard

Q10. A particle enters a vertical loop of radius \(R\) with speed \(\sqrt{11gR}\). Normal reaction at top of loop is

A. \(6mg\)

B. \(5mg\)

C. \(4mg\)

D. \(7mg\)

🎯 Free Trail Quiz