question_answer

Which would require a greater force accelerating a body of 10 g mass at \[\text{5 m}/{{\text{s}}^{\text{2}}}\]or a body of 20 g mass at\[\text{2 m}/{{\text{s}}^{\text{2}}}\]?

Answer:

Case-1	Case-2
Mas of the first body, \[{{m}_{1}}=10g\] \[=10/100\] \[=1/100\,kg\]	Mass of the second body,\[s=1mm={{10}^{3}}m,\text{ }m=4mg=4\times {{10}^{3}}g,\] \[=20/1000\] \[=1/50\,kg\]
acceleration on first \[body,\,\,{{a}_{1}}=5m/{{s}^{2}}\]	Acceleration on second body, \[{{a}^{2}}=2m/{{s}^{2}}\]
Force on the first body, \[{{F}_{1}}=?\]	Force acting on second body, \[{{F}_{2}}=?\]
We know that, \[F=ma\]

Applying the formula in both the cases,

\[{{F}_{1}}={{m}_{1}}\times {{a}_{1}}\]	\[{{F}_{2}}={{m}_{2}}\times {{a}_{2}}\]
\[\Rightarrow {{F}_{1}}=\frac{1}{100}\times 5\]	\[\Rightarrow {{F}_{2}}=\frac{1}{50}\times 2\]
\[\Rightarrow {{F}_{1}}=\frac{1}{20}N\]	\[\Rightarrow {{F}_{2}}=\frac{1}{25}N\]
\[\therefore {{F}_{1}}=\frac{1}{20}N\]	\[{{F}_{2}}=0.04N\]

\[\therefore {{F}_{1}}>{{F}_{2}}\] \[\therefore 10\,\,g\] mass accelerating at \[5m/{{s}^{2}}\]requires greater force.