A block is on a frictionless table,on earth.The block accelerates at 5.3 m/ $\mathrm { s }^2$ when a $10 \mathrm {~N}$ horizontal force is exerted on it.The block and table are set up on the Moon where the acceleration of objects due to the gravitational attraction is 1.62 m/ $\mathrm { s }^2$ A horizontal force of 5 N is now exerted on the block when it is on the Moon.The acceleration of the block due to this force is closest to
A)2.7 m/ $\mathrm { s }^2$
B)2.4 m/ $\mathrm { s }^2$
C)2.9 m/ $\mathrm { s }^2$
D)3.2 m/ $\mathrm { s }^2$
E)3.4 m/ $\mathrm { s }^2$

Question

Quizplus · Accepted Answer

The acceleration of the block on Earth is given by $a = \frac{F}{m}$, where $F = 10 \, \text{N}$ and $a = 5.3 \, \text{m/s}^2$. This gives us the mass $m = \frac{F}{a} = \frac{10}{5.3}$. On the Moon, the same mass is subjected to a 5 N force, so the acceleration $a_{\text{Moon}} = \frac{F_{\text{Moon}}}{m} = \frac{5}{10/5.3} = 2.65 \, \text{m/s}^2$, which is closest to 2.7 m/s².

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