Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A scooter weighing 150 kg together with its rider moving at 36 km/h is to take a turn of radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Convert the speed from km/h to m/s.
36 km/h = \frac{36 \times 1000}{3600} = 10 \text{ m/s}.
Step 2: Use the formula for centripetal force, which is needed to keep the scooter moving in a circular path. The formula is given by:
\[ F_c = \frac{m v^2}{r} \]
where:
- \( F_c \) is the centripetal force,
- \( m \) is the mass of the scooter and rider (150 kg),
- \( v \) is the velocity (10 m/s),
- \( r \) is the radius of the turn (30 m).
Step 3: Substitute the values into the centripetal force formula:
\[ F_c = \frac{150 \times 10^2}{30} \]
\[ F_c = \frac{150 \times 100}{30} = \frac{15000}{30} = 500 \text{ N} \]
Step 4: Therefore, the horizontal force needed to make the turn possible is 500 N.
36 km/h = \frac{36 \times 1000}{3600} = 10 \text{ m/s}.
Step 2: Use the formula for centripetal force, which is needed to keep the scooter moving in a circular path. The formula is given by:
\[ F_c = \frac{m v^2}{r} \]
where:
- \( F_c \) is the centripetal force,
- \( m \) is the mass of the scooter and rider (150 kg),
- \( v \) is the velocity (10 m/s),
- \( r \) is the radius of the turn (30 m).
Step 3: Substitute the values into the centripetal force formula:
\[ F_c = \frac{150 \times 10^2}{30} \]
\[ F_c = \frac{150 \times 100}{30} = \frac{15000}{30} = 500 \text{ N} \]
Step 4: Therefore, the horizontal force needed to make the turn possible is 500 N.
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