Why are mountain roads generally made winding upwards rather than going straight up?

Two inclined frictionless tracks,one gradual and the other steep,meet at $A$ from where two stones are allowed to slide down from rest,one on each track. Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ},$ and $h=10 \; m,$ what are the speeds and times taken by the two stones?

$A$ block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of the force exerted by the plane on the block is

$A$ block of mass $200\, g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F = \sqrt{x}\, N$ as shown in the figure. The value of $x = .....$

An object requires $500 \,N$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined plane at a constant speed. The weight of the object is

$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is