question_answer

A 2 kg cylinder rests on a cart as shown in the figure. The coefficient of static friction between the cylinder and the cart is \[0.5.\] The cylinder is 4 cm in diameter and 10 cm in height. The minimum acceleration of the cart needed to make the cylinder tip over is about:

A) \[2m/{{s}^{2}}\]                     

B) \[4m/{{s}^{2}}\]

C) \[6m/{{s}^{2}}\]                     

D) \[8m/{{s}^{2}}\]

Correct Answer: B

Solution :

[d] If a is the acceleration of the cart, then \[ma\frac{h}{2}=mg\times r\] \[\Rightarrow a=\frac{2gr}{h}=\frac{2\times 10\times 2}{10}=4m/{{s}^{2}}\]