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Physics Chapter 4 : Topic 5
Centripetal Force
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Centripetal force is defined as:
Reasoning: Centripetal force is the inward force needed to maintain circular motion.
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The direction of centripetal force is:
Reasoning: Centripetal force always acts radially inward.
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The formula for centripetal force using linear velocity is:
Reasoning: Centripetal force depends on mass, square of velocity, and inverse of radius.
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The formula for centripetal force using angular velocity is:
Reasoning: Since $\mathbf{v}\mathbf{=}\mathbf{r\omega}$, substituting into $\mathbf{F}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$ gives $\mathbf{F}\mathbf{=}\mathbf{mr}\mathbf{\omega}^{\mathbf{2}}$.
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If the mass of an object moving in a circle doubles, centripetal force becomes:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{\propto}\mathbf{m}$ $\mathbf{\Longrightarrow}$ Force increases directly with mass.
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The SI unit of centripetal force is:
Reasoning: Force is measured in Newtons.
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If the velocity of an object is doubled, centripetal force becomes:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$ ; Force depends on the square of velocity.
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If the radius of circular motion is doubled while velocity remains constant, centripetal force becomes:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{\propto}$ $\frac{\mathbf{1}}{\mathbf{r}}$ ; Increasing radius decreases force.
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A car moving on a circular road requires centripetal force provided by:
Reasoning: Static friction provides the inward force needed for turning.
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A satellite revolving around Earth is kept in orbit by:
Reasoning: Earth’s gravity acts as the centripetal force.
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A $\mathbf{2\ kg}$ object moves in a circle of radius $\mathbf{4\ m}$ with velocity $\mathbf{8\ m/s}$. Centripetal force is:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$ $\mathbf{\Longrightarrow}$ $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{2}\mathbf{(8)}^{\mathbf{2}}}{\mathbf{4}}$ $\mathbf{\Longrightarrow}$ $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{128}}{\mathbf{4}}\mathbf{= 3}\mathbf{2\ N}$
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A $\mathbf{5\ kg}$ object moves with speed $\mathbf{10\ m/s}$ in a circle of radius $\mathbf{2\ m}$. Force required is:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}\mathbf{=}\frac{\mathbf{5}\mathbf{(10)}^{\mathbf{2}}}{\mathbf{2}}\mathbf{=}\frac{\mathbf{500}}{\mathbf{2}}\mathbf{= 250\ N}$
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A $\mathbf{3\ kg}$ object rotates with angular velocity $\mathbf{4\ rad/s}$ at radius $\mathbf{2\ m}$. Centripetal force is:
Reasoning: $\mathbf{F}\mathbf{=}\mathbf{mr}\mathbf{\omega}^{\mathbf{2}}$ $\mathbf{= 3(2)}\mathbf{(4)}^{\mathbf{2}}\mathbf{= 96\ N}$
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A body of mass $\mathbf{10\ kg}$ moves in a circle of radius $\mathbf{5\ m}$ with velocity $\mathbf{5\ m/s}$. Centripetal force is:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}\mathbf{=}\frac{\mathbf{10}\mathbf{(5)}^{\mathbf{2}}}{\mathbf{5}}\mathbf{=}\frac{\mathbf{250}}{\mathbf{5}}\mathbf{= 50\ N}$
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An object experiences centripetal force of $\mathbf{40\ N}$ when moving at $\mathbf{4\ m/s}$ in a circle of radius $\mathbf{2\ m}$. Its mass is:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$ $\mathbf{\Longrightarrow}$ $\mathbf{40 =}$ $\frac{\mathbf{m}\mathbf{(4)}^{\mathbf{2}}}{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{40 =}$ $\frac{\mathbf{m}\mathbf{(16)}}{\mathbf{2}}$$\mathbf{40 = 8}\mathbf{m}$ $\mathbf{\Longrightarrow}$ $\mathbf{m}\mathbf{= 5\ kg}$
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A body rotates with angular velocity $\mathbf{5\ rad/s}$, radius $\mathbf{3\ m}$, and mass $\mathbf{2\ kg}$. The centripetal force is:
Reasoning: $\mathbf{F}\mathbf{=}\mathbf{mr}\mathbf{\omega}^{\mathbf{2}}$ $\mathbf{= 2(3)(25) = 150N}$
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Centripetal force does not increase the speed of an object because it is:
Reasoning: A perpendicular force changes direction but not speed.
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In uniform circular motion, centripetal force changes:
Reasoning: Velocity changes because its direction continuously changes.
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If centripetal force acting on an object suddenly disappears, the object moves:
Reasoning: Due to inertia, the object continues in its instantaneous direction.
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Centripetal force is not a new type of force because:
Reasoning: Gravity, tension, friction, etc., can act as centripetal force.
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A stone tied to a string is rotated in a circle. The centripetal force is provided by:
Reasoning: The tension pulls the stone toward the center.
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Increasing angular velocity of a rotating object causes centripetal force to:
Reasoning: $\mathbf{F}\mathbf{=}\mathbf{mr}\mathbf{\omega}^{\mathbf{2}}$ ; Force depends on square of angular velocity.
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If angular velocity becomes three times, centripetal force becomes:
Reasoning: $\mathbf{F}\mathbf{\propto}\mathbf{\omega}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{3}^{\mathbf{2}}\mathbf{= 9}$
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A larger radius requires less centripetal force when:
Reasoning: At constant velocity: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$
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The centripetal force on an object in circular motion is maximum when:
Reasoning: Force depends on $\mathbf{v}^{\mathbf{2}}$.
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A rotating object has constant speed but changing velocity because:
Reasoning: The inward force continuously changes velocity direction.
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Which quantity determines the direction of centripetal force?
Reasoning: Centripetal force always points toward the center.
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The work done by centripetal force in uniform circular motion is:
Reasoning: Force and displacement are perpendicular.
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If the radius of a circular path approaches zero, centripetal force:
Reasoning: $\mathbf{F}_{\mathbf{c}}\mathbf{=}$ $\frac{\mathbf{m}\mathbf{v}^{\mathbf{2}}}{\mathbf{r}}$ $\mathbf{\Longrightarrow}$ Smaller radius requires greater force.
30 / 30
Which statement correctly describes centripetal force?
Reasoning: Centripetal force is inward and maintains circular motion.
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