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Question

A car is moving on a circular road of diameter 50 m with a speed of 5 m/s. It is suddenly accelerated at a rate of $$\displaystyle 1\ { m }/{ { s }^{ 2 } }$$. If the mass of the car is 500 kg, then the net force acting on the car is:


A
5 N
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B
1000 N
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C
5002 N
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D
5002 N
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Solution

The correct option is B $$\displaystyle 500\sqrt { 2 } \ N$$
Given,  $$\displaystyle r=25\ m, v=5\ m/s, m=500\ kg$$
$$\displaystyle { a }_{ t }=1\ { m }/{ { s }^{ 2 } }, { a }_{ r }=\frac { { v }^{ 2 } }{ r } =\frac { 5\times 5 }{ 25 } =1\ { m }/{ { s }^{ 2 } }$$
$$\displaystyle { a }_{ net }=\sqrt { { a }_{ t }^{ 2 }+{ a }_{ r }^{ 2 } } =\sqrt { { 1 }^{ 2 }+{ 1 }^{ 2 } } =\sqrt { 2 }\  { m }/{ { s }^{ 2 } }$$
$$\displaystyle F={ ma }_{ net }=500\sqrt { 2 } \ N$$

Physics

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