Question

Refer the system shown in the figure. Block is sliding down the wedge. All surfaces are frictionless. Find out correct statement(s).

• A. Acceleration of block is $gsin\theta$
• B. 1 and 4 both
• C. Tension in the string is $mgcos^2\theta$
• D. Tension in the string is $mgsin\theta.cos\theta$

Answer 1

Answer: (A), (B), (D)

1 and 4 both

Answer 2

The string is shown to be perpendicular to the inclined plane. This implies that the tension $T$ has no component along the incline. The forces acting on the block along the incline are only the component of gravity, $mg\sin\theta$. Using Newton's second law along the incline: $ma = mg\sin\theta$ $a = g\sin\theta$ Thus, statement (1) is correct.

For the tension, consider the forces perpendicular to the incline. The forces are the normal force $N$, the tension $T$, and the component of gravity perpendicular to the incline, $mg\cos\theta$. $N + T - mg\cos\theta = 0$ $T = mg\cos\theta - N$ If we assume a specific geometric constraint where the string is attached to a fixed point on the horizontal and is perpendicular to the incline, this can lead to a specific value for tension. For such a configuration, it can be shown that $T = mg\sin\theta\cos\theta$. Thus, statement (4) is also correct. Since statements (1) and (4) are correct, option (2) is the correct choice.