Category: HC Verma Part 1: Mechanics

Problem Statement Solve the kinematics problem: A 2 kg block is on a smooth wedge of mass 5 kg and inclination 30°. The wedge is on a frictionless surface. Find the acceleration of the wedge. Constraint relation; normal force between block and wedge; Newton’s law for wedge Step 1: Let the wedge acceleration be $A$…

Problem Statement Solve the Newton’s Laws / mechanics problem: A person stands on a floor. List all action-reaction pairs involving the person. Newton’s third law: action and reaction are equal, opposite, and act on different bodies Pair 1: Earth pulls person downward (gravity) — Person pulls Earth upward (same magnitude). Pair 2: Floor pushes person…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block of mass 5 kg is pulled by a string over a pulley. The other side has a 3 kg mass hanging. The 5 kg block is on a rough horizontal surface ($\mu_k = 0.3$). Find $a$ and $T$. ($g = 10$ m/s²) $m_2 g…

Problem Statement Solve the Newton’s Laws / mechanics problem: Two blocks, $m_1 = 4$ kg and $m_2 = 6$ kg, are on a frictionless horizontal surface connected by a string. A force $F = 20$ N is applied on $m_2$. Find acceleration and tension. $a = F/(m_1+m_2)$; $T = m_1 a$ Step 1: $a =…

Problem Statement Solve the Newton’s Laws / mechanics problem: Two masses $m_1 = 3$ kg and $m_2 = 5$ kg are connected by a string over a pulley. $m_1$ is on a frictionless incline of 30° and $m_2$ hangs freely. Find the acceleration and tension. ($g = 10$ m/s²) $m_2 g – T = m_2…

Problem Statement Solve the Newton’s Laws / mechanics problem: Draw and analyze the free body diagram of a 3 kg block on a frictionless incline of 45°. Find the acceleration. ($g = 10$ m/s²) Forces: weight ($mg$ downward), normal force ($N$ perpendicular to incline) $a = g\sin\theta$ Step 1: Forces on block: weight $mg =…

Problem Statement Solve the momentum/collision problem: A ball of mass 0.2 kg hits a wall at 10 m/s and bounces back at the same speed. Find the change in momentum (impulse). Impulse = change in momentum = $m(v_f – v_i)$ Step 1: Taking toward wall as positive: $p_i = 0.2 \times 10 = 2$ kg…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 1000 kg car accelerates from 0 to 72 km/h in 10 s on a frictionless road. Find the force required. $v = u + at$; $F = ma$ Step 1: $v = 72$ km/h $= 20$ m/s; $u = 0$; $t = 10$ s. Step…

Problem Statement Solve the Newton’s Laws / mechanics problem: A net force of 40 N acts on a 8 kg body. Find the acceleration. $F = ma \Rightarrow a = F/m$ Step 1: $a = F/m = 40/8 = 5$ m/s². $$\boxed{a = 5\text{ m/s}^2}$$ Given Information Mass(es), forces, angles, and coefficients of friction as…

Problem Statement Solve the Newton’s Laws / mechanics problem: A body is at rest. What is the net force on it? A body moves with constant velocity — what is the net force on it? Newton’s first law: $F_{net} = 0$ for constant velocity (including zero velocity) Step 1: At rest: acceleration = 0; by…