A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity)
Gymnosperms are flowerless plants that produce cones and seeds. It literally means "naked seed". They sit exposed on the surface of leaf-like structures called bracts. Gymnosperms are vascular plants of the subkingdom Embyophyta and include conifers, cycads, ginkgoes, and gnetophytes. They are abundant in temperate forest and boreal forest biomes with species that can tolerate moist or dry conditions.