Work-energy-power practice · Medium

Option B ($40 \text{{ Nm}}^{-1}$) is correct because the potential energy lost by the block equals the potential energy stored in the spring when it's compressed.

Option C (If Assertion is True but the Reason is False) is correct because the resultant acceleration is towards the center, but a vector can change without rotation.

Option D is correct because linear momentum is always conserved in collisions if no external forces are acting, even in inelastic collisions.

Option A ($0.1\mathrm{\;m}{\mathrm{s}^{ - 1}}$) is correct because the speed is calculated by equating the work done to the kinetic energy gained by the ship.

Option D is correct because the road does not undergo any displacement, so no work is done by the motorcycle on the road.

Option D (If both Assertion & Reason are false) is correct because work done by a conservative force is path-independent, and not all conservative forces are central forces.

Option D is correct. The assertion is incorrect because constant power implies non-uniform acceleration, while the reason is correct as it states the work-energy theorem.

Option D (4 sec) is correct because it is calculated using the formula for the time period of revolution in a vertical circle.

Option A is correct because momentum conservation leads to the ratio of kinetic energies being the inverse ratio of masses.

Option C (Linear momentum of system) is correct because, in all types of collisions, the total linear momentum of the system remains conserved due to the absence of external forces.

Option B (Minimum potential energy) is correct because stable equilibrium corresponds to the lowest potential energy state.

Option C (Momentum) is correct because in the absence of external forces, the total momentum of a system remains conserved, even during an explosion.

Option D (The first ball will move with a velocity less than $\bar{u}_1$) is correct because in an elastic collision with equal masses, the balls exchange velocities, making it impossible for the first ball to move with a velocity less than its initial velocity.

Option D (8 F) is correct because when both the length of the string and angular velocity are doubled, the tension becomes 8 times the original tension.

Option B is correct because while both the assertion and reason are true, the reason doesn't fully explain the assertion. Conservative forces are path-independent, and central forces are examples, but the latter doesn't explain the former.

Option A ($25 \%$) is correct because it is calculated by finding the percentage difference between the initial and final potential energies.

Option D is correct. The force is non-conservative, meaning the potential energy function is not defined because the work done depends on the path taken.

Option B ($20 \sqrt{3} \mathrm{~m} / \mathrm{s}$) is correct because the velocity is calculated by equating potential and kinetic energies.

Option C ($v=\left(\frac{{3 x P}}{{m}}\right)^{1 / 3}$) is correct because it is derived from the relationship between power, force, and velocity, considering constant power and integrating with respect to distance.

Option B ($2y-x$) is the correct answer because it is derived by setting up equations based on the relationship between tension and length, and then solving for the length when the tension is 9 N.

Option B ($12 \mathrm{~m} \mathrm{s}^{-1}$) is correct because it is calculated using the principle of conservation of linear momentum.

Option A (2115 N) is correct because it is the result of calculating the centripetal force using the formula F = mv²/r, with proper unit conversions.

Option B (10.84 m/s) is correct because it is calculated using the formula for maximum speed on a curved road, considering the coefficient of friction and the radius of the turn.

Option A (If both Assertion and Reason are true and Reason is correct explanation of Assertion) is correct because the force is due to the change in momentum during the elastic collision.

Option D is correct. In non-uniform circular motion, the acceleration vector has both radial and tangential components. The angle between the position vector and the acceleration vector can be any value between 0 and 180 degrees, excluding 90 degrees. 135 degrees is a valid angle.

Option A ($64 \mathrm{~J}$) is correct because it calculates the work done using the work-energy theorem, finding the final velocity after 2 seconds.

Option A ($3.2 \mathrm{~ms}^{-2}$) is correct because it calculates the net acceleration by combining the tangential and centripetal accelerations vectorially.

Option A ($\mathbf{\vec F}.{\overrightarrow {\mathbf{dr}}} = x\,\,dx + y\,\,dy$) is correct because it represents the dot product of the force vector and the displacement vector, which equals the work done.

Option A (first increases then decreases to zero) is correct because when the man jumps, he initially exerts a force on the platform, increasing the reading, and then the reading returns to zero as he leaves the platform.

Option C is correct because the angular frequency is calculated from the second derivative of the potential energy at the equilibrium point.