(B) Derivation: According to Newton's second law,$F \propto \frac{dp}{dt}$. Since $p = mv$,$F = k \frac{d(mv)}{dt} = kma$. Taking $k=1$,we get $F = ma

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(B) Derivation: According to Newton's second law,$F \propto \frac{dp}{dt}$. Since $p = mv$,$F = k \frac{d(mv)}{dt} = kma$. Taking $k=1$,we get $F = ma$.$(i)$ Given: $m = 10 \, g = 0.01 \, kg$,$u = 10^3 \, m \, s^{-1}$,$v = 0$,$s = 5 \, cm = 0.05 \, m$.Using $v^2 - u^2 = 2as$:$0^2 - (10^3)^2 = 2 \cdot a \cdot 0.05$$-10^6 = 0.1 \cdot a$$a = -10^7 \, m \, s^{-2}$.Resistive force $F = |ma| = 0.01 \times 10^7 = 10^5 \, N$.$(ii)$ Using $v = u + at$:$0 = 10^3 + (-10^7) \cdot t$$10^7 \cdot t = 10^3$$t = 10^{-4} \, s$.

Class 9 Science FORCE AND LAWS OF MOTION Mix Example - FORCE AND LAWS OF MOTION

Difficult

Using the second law of motion,derive the relation between force and acceleration. $A$ bullet of $10 \, g$ strikes a sandbag at a speed of $10^3 \, m \, s^{-1}$ and gets embedded after traveling $5 \, cm$. Calculate:
$(i)$ The resistive force exerted by the sand on the bullet.
$(ii)$ The time taken by the bullet to come to rest.

A
$10^{2} \, N, 10^{-2} \, s$
B
$10^{5} \, N, 10^{-4} \, s$
C
$10^{6} \, N, 10^{-6} \, s$
D
$10^{7} \, N, 10^{-7} \, s$

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FORCE AND LAWS OF MOTION

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Mix Example - FORCE AND LAWS OF MOTION

State the law of conservation of momentum. How does conservation of momentum take place in each of the following?
$(i)$ $A$ rocket taking off from ground.
$(ii)$ Flying of a jet aeroplane.

Medium

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State whether the following statement is true or false:
The force of friction is smaller in solids than in liquids.

Easy

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In which direction do the following forces act when an object is in motion?
$(i)$ Frictional force
$(ii)$ Gravitational force
$(iii)$ Centripetal force

Medium

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$(a)$ Using Newton's law of motion, derive the relation between force and acceleration.
$(b)$ Define one newton.
$(c)$ Which would require a greater force to accelerate: a $0.5 \, kg$ mass at $5 \, m s^{-2}$ or a $4 \, kg$ mass at $2 \, m s^{-2}$? Give reason.

Difficult

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$A$ large truck and a car,both moving with speed $v$,have a head-on collision and both of them come to a halt after that. If the collision lasts for $10 \ s$:
$(i)$ Which vehicle experiences the greater force of impact?
$(ii)$ Which vehicle experiences the greater momentum change?
$(iii)$ Which vehicle experiences the greater acceleration?
$(iv)$ Why is the car likely to suffer more damage than the truck?

Medium

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Similar Questions

State the law of conservation of momentum. How does conservation of momentum take place in each of the following?$(i)$ $A$ rocket taking off from ground.$(ii)$ Flying of a jet aeroplane.

State whether the following statement is true or false:The force of friction is smaller in solids than in liquids.

In which direction do the following forces act when an object is in motion?$(i)$ Frictional force$(ii)$ Gravitational force$(iii)$ Centripetal force

$(a)$ Using Newton's law of motion, derive the relation between force and acceleration.$(b)$ Define one newton.$(c)$ Which would require a greater force to accelerate: a $0.5 \, kg$ mass at $5 \, m s^{-2}$ or a $4 \, kg$ mass at $2 \, m s^{-2}$? Give reason.

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State the law of conservation of momentum. How does conservation of momentum take place in each of the following?
$(i)$ $A$ rocket taking off from ground.
$(ii)$ Flying of a jet aeroplane.

State whether the following statement is true or false:
The force of friction is smaller in solids than in liquids.

In which direction do the following forces act when an object is in motion?
$(i)$ Frictional force
$(ii)$ Gravitational force
$(iii)$ Centripetal force

$(a)$ Using Newton's law of motion, derive the relation between force and acceleration.
$(b)$ Define one newton.
$(c)$ Which would require a greater force to accelerate: a $0.5 \, kg$ mass at $5 \, m s^{-2}$ or a $4 \, kg$ mass at $2 \, m s^{-2}$? Give reason.