question_answer

A car is moving in a circular path of radius 500 m wih a speed of 30 m/s. If the speed is increasing, at the rate of \[\text{2 m}/{{\text{s}}^{\text{2}}},\] the resultant acceleration will be

A) \[\text{2 m}/{{\text{s}}^{\text{2}}}\]                                    

B)  \[\text{2}.\text{5 m}/{{\text{s}}^{\text{2}}}\]

C) \[\text{2}.\text{7 m}/{{\text{s}}^{\text{2}}}\]                                   

D)  \[\text{4 m}/{{\text{s}}^{\text{2}}}\]

Correct Answer: C

Solution :

                 A body moving in circular motion, has radial \[({{a}_{R}})\] and tangential acceleration \[({{a}_{T}})\], Hence, resultant acceleration is given by                 \[a=\sqrt{a_{T}^{2}+a_{R}^{2}}\] Given,   \[{{a}_{T}}=2m/{{s}^{2}}\],                 \[{{a}_{R}}=\frac{{{V}^{2}}}{r}=\frac{30\times 30}{500}=1.8\,m/{{s}^{2}}\] \[\therefore \]  \[a=\sqrt{{{(1.8)}^{2}}+{{(2)}^{2}}}=\sqrt{7.24}\] \[\Rightarrow \]               \[a=2.69\approx 2.7\,m/{{s}^{2}}\]