Mock Test 2 — Work, Energy and Power

A particle of $m = 1$ kg moves under $F = -kx$ (SHM) with $k = 100$ N/m. Maximum velocity at $x = 0$ if amplitude = $0.1$ m:

A ball is projected at $u$ from ground at $\theta$. At max height, KE equals:

A body of $m$ slides down a smooth quarter-circle of radius $R$ from top. Speed at bottom:

A car of $1000$ kg accelerates uniformly from rest to $20$ m/s in $5$ s. Average power developed:

A particle's PE is $U(x) = (x^2 - 6x) $ J. The position of stable equilibrium:

A ball of mass $m$ at rest is bombarded by another of mass $2m$ at velocity $v$, in elastic collision head-on. Velocity of $m$ after:

A 2D elastic collision between equal masses, one initially at rest: after collision, velocity vectors are:

A vertical chain of mass $M$, length $L$ is held by upper end. When released, the speed of any point distance $x$ from upper end when it has just fallen $x$:

A body of mass $0.5$ kg at $4$ m/s collides with $1$ kg at rest. After collision, both move with same velocity. The collision is:

Ball thrown horizontally from $20$ m height with $10$ m/s. Speed on impact ($g = 10$):

A man weighing $60$ kg climbs $20$ m in $40$ s. Power developed (W, $g = 10$):

A bullet at $400$ m/s penetrates $10$ cm in wood. If fired into double thickness ($20$ cm) of same wood at $400$ m/s, the depth of penetration (cm):

A ball is dropped from $80$ m on a hard floor. Coefficient of restitution = $0.5$. Maximum height attained after first rebound (m):

Assertion (A): Power output of a constant-force engine increases linearly with speed. Reason (R): Power = force × velocity.

Assertion (A): In an elastic collision between equal masses, one initially at rest, after collision, they have perpendicular velocity vectors. Reason (R): Conservation of momentum and KE together imply perpendicularity for equal masses.