Mock Test 2 — Laws of Motion

A block of mass $m$ is placed on a wedge of angle $\theta$, mass $M$, on a smooth floor. A horizontal force $F$ on the wedge keeps the block stationary on the wedge. The required $F$:

Two blocks $m_1 = 1$ kg and $m_2 = 2$ kg are connected over a pulley. $m_1$ is on a smooth horizontal table; $m_2$ hangs. Acceleration ($g = 10$):

A bead of mass $m$ slides on a smooth wire bent into a circle of radius $R$ in a vertical plane. At the bottom, it has velocity $\sqrt{6gR}$. Normal force from wire at the top:

A man of mass $80$ kg stands in a lift accelerating upward at $5 \text{ m/s}^2$. If the man jumps with a velocity of $2$ m/s relative to the lift, his velocity relative to ground is ($g = 10$):

A block of mass $m$ is on a rough horizontal surface ($\mu$). The minimum force at angle $\theta$ above horizontal needed to just move it:

In a vertical circle of radius $R$, a particle at horizontal level of the centre has minimum speed (no break) of:

A box of mass $5$ kg is placed on a truck's floor. $\mu_s = 0.3$. The truck accelerates uniformly. Maximum acceleration of truck so that the box doesn't slip ($g = 10$):

A bullet of $50$ g penetrates $5$ cm into a wooden block. To penetrate $20$ cm, its velocity should be:

Two blocks connected by spring on smooth surface. $m_1 = 1$, $m_2 = 2$. A force $9$ N is applied on $m_1$. Acceleration of $m_2$ when spring extends at maximum:

A car negotiates a banked road of $30^\circ$, radius $20$ m. The car's speed for no friction needed ($g = 10$):

A bullet of mass $10$ g moving at $400$ m/s strikes a wood block ($1.99$ kg) at rest and embeds. Common velocity after collision (m/s):

A car of mass $1000$ kg travels around a horizontal circular track of $50$ m at $20$ m/s. Centripetal force (N) acting on it:

A block of $2$ kg on a rough horizontal surface ($\mu = 0.5$). A horizontal force $20$ N is applied, then removed when velocity is $10$ m/s. The distance the block slides after force is removed (m, $g = 10$):

Assertion (A): In a rotating frame, a pseudo-force called the centrifugal force exists. Reason (R): In any non-inertial frame, pseudo-forces must be added to apply Newton's second law.

Assertion (A): Conservation of linear momentum holds when net external force is zero. Reason (R): Internal forces between parts of a system cancel pairwise by Newton's third law.