NEET Physics — Laws of Motion

A \( 0.4 \, \text{kg} \) ball at \( 40 \, \text{m/s} \) hits a wall at \( 45^\circ \) and rebounds at \( 30^\circ \) with speed \( 35 \, \text{m/s} \). What is the impulse along the wall? (Take \( \sin 45^\circ = \cos 45^\circ = 0.707 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

A \( 1000 \, \text{kg} \) car on a \( 30^\circ \) banked road (\( \mu_s = 0.35 \)) turns at radius \( 50 \, \text{m} \) while decelerating at \( 2 \, \text{m/s}^2 \) tangentially. What is the maximum speed? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 30^\circ = 0.577 \))

A \( 3.5 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is connected to a \( 5.5 \, \text{kg} \) mass over a pulley. A \( 8 \, \text{N} \) force aids the \( 3.5 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

A \( 8 \, \text{kg} \) block on a \( 60^\circ \) incline (\( \mu_k = 0.25 \)) is connected to a \( 5 \, \text{kg} \) mass over a pulley. A \( 20 \, \text{N} \) force at \( 30^\circ \) to the incline opposes the \( 8 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 60^\circ = 0.866 \), \( \cos 60^\circ = 0.5 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

A \( 7.6 \, \text{kg} \) block on a \( 60^\circ \) incline (\( \mu_k = 0.15 \)) is pulled upward by a \( 9.6 \, \text{kg} \) mass over a pulley. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 60^\circ = 0.866 \), \( \cos 60^\circ = 0.5 \))