Newton's Laws of Motion

780 N

Step 1: Identify the situation — lift accelerates upward, so apparent weight > real weight. Step 2: Formula: W_apparent = m(g + a) when lift accelerates upward. Step 3: W_apparent = 60 × (10 + 3) = 60 × 13 = 780 N. Why wrong options are incorrect: - 420 N: Used m(g - a) = 60 × 7, formula for downward acceleration. - 600 N: This is actual weight mg = 60 × 10, ignores acceleration. - 180 N: Only calculated m × a = 60 × 3, forgot to add gravity.

2 m/s

Step 1: Convert mass of bullet: m_bullet = 50 g = 0.05 kg. Mass of gun M = 5 kg. Step 2: Apply conservation of linear momentum. Initial momentum = 0 (both at rest). Step 3: Final momentum: m_bullet × v_bullet + M × V_gun = 0. 0.05 × 200 + 5 × V_gun = 0. Step 4: 10 + 5 × V_gun = 0 → V_gun = -10/5 = -2 m/s. Magnitude of recoil velocity = 2 m/s. Why wrong options are incorrect: - 1 m/s: Forgot to convert grams to kg. - 4 m/s: Divided bullet velocity by gun mass directly (4 = 200/50). - 0.5 m/s: Calculated 0.05/5 × 200 = 0.02 × 200 incorrectly.

A body at rest remains at rest and a body in uniform motion continues in uniform motion unless acted upon by an external unbalanced force.

Newton's First Law (Law of Inertia) states that an object at rest stays at rest and an object in uniform motion stays in uniform motion along a straight line unless compelled by an external unbalanced force. Why wrong options are incorrect: - Option A is incomplete — it ignores the case of a body at rest and also doesn't specify 'unbalanced' force. - Option C is Newton's Third Law (Law of Action-Reaction). - Option D is Newton's Second Law (F = dp/dt).

5 m/s²

Step 1: On a smooth inclined plane, only the component of gravity along the plane causes acceleration. Step 2: The component along the plane = mg sin θ. Step 3: Applying Newton's second law: mg sin θ = ma → a = g sin θ. Step 4: a = 10 × sin 30° = 10 × 0.5 = 5 m/s². Why wrong options are incorrect: - 10 m/s²: This is 'g' itself, ignoring the incline angle. - 8.66 m/s²: This uses g cos 30° = 10 × 0.866, which is the component perpendicular to the plane (normal reaction direction). - 2.5 m/s²: This is g sin 30° / 2, an incorrect halving of the answer.