Physics || Shashaank Blogspot

 

1 ) Two masses of 40 kg and 30 kg are connected by a weightless string passing over a friction less pulley as shown in the figure. The acceleration of the system would be:

Gravitation force on A, FA​=mgsin30=40×10×0.5=200N

Gravitation force on B, FB​=Mgsin30=30×10×0.5=150N

Fnet​=FA​−FB​

⇒(M+m)a=FA​−FB​

⇒a=M+mFA​−FB​​=40+30200−150​=0.71ms−2

Hence, acceleration of the system is 0.71ms−2 

Acceleration of the particle when its velocity becomes half of the initial velocity. 

$V=-\left(\frac{20}{50}\right)x$

$V=\frac{-2x}{5}$

$a=\frac{dv}{dt}=\frac{-2}{5}\frac{dx}{dt}=\frac{-2V}{5}$

$a=\frac{-2V}{5}$

initial velocity $\left(u\right)=20m/s$

$\frac{u}{2}=10m/s$

$a=\frac{-2}{5}\left(10\right)=-4m/s^2$.

A model airplane with mass 0.750 kg is tethered to the ground by a wire so that it flies in a horizontal circle 30.0 m in radius. The airplane engine provides a net thrust of 0.800 N perpendicular to the tethering wire.
Find the torque the net thrust produces about the center of the circle.