Question

When a horizontal force $P$ acts on a cart of mass $20\text{kg}$, it moves with a uniform velocity on a horizontal floor. When a force of $1.2P$ acts on the cart, it moves with an acceleration of $0.05{\text{m/s}}^2$. Find the value of $P$.

• A. $2\text{N}$
• B. $3\text{N}$
• C. $5\text{N}$
• D. $4\text{N}$

Answer 1

The correct option is C $5\text{N}$

When force $P$ is applied, the cart moves with uniform velocity.
$\Rightarrow F_{\text{net}}=0$

$\Rightarrow P-f=0$

$\Rightarrow f=P...\left(1\right)$

Also, when force $1.2P$ is applied, the cart moves with an acceleration of $0.05{\text{m/s}}^2$.

$\Rightarrow F_{\text{net}}=ma$

$\Rightarrow 1.2P-f=ma$

$\Rightarrow 1.2P-P=ma\left[\text{From}1\right]$

$\Rightarrow 0.2P=20\times 0.05$

$\Rightarrow P=5\text{N}$