Question

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is pushed slightly towards right. Its speed when it reaches the point B is ($g=10m{s}^{-2}$)

• A. 10 m/s
• B. $\sqrt{10}m/s$
• C. $20m{s}^{-1}$
• D. $\sqrt{20}m{s}^{-1}$

Answer 1

The correct option is B $\sqrt{10}m/s$

Potential energy of A is $mgh=m\times 10\times 1=10m$

Kinetic energy at $A=0$

Mechanical energy at $A=10m+0=10m$

Potential energy of $B=mgh=m\times 10\times 5=5m$

Kinetic energy at B is $10m-5m=5m$

Hence Velocity (for speed)

$\frac{1}{2}m{v}^2=5m$

$\frac{1}{2}{v}^2=5$

$v^2=5\times 2$

$v=\sqrt{10}$