A U-tube containing a liquid is accelerated horizontally with a constant acceleration α₀. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

A wooden block of mass 0.5 kg and density 800 kg m^-3 is fastened to the free end of a vertical spring of spring constant 50 N m^-1 fixed at the bottom. If the entire system is completely immersed in water find (a) the elongation (for compression) of the spring in equilibrium and (b) the time-period of vertical oscillations of the block when it is slightly depressed and released.

A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagjrathi and becomes river Ganga. Suppose Alaknanda has a width of 12 m, Bhagirathi has a width of 8 m and Ganga has a width of 16 m. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be 20 km h^-1 and in Bhagirathi be 16 km h^-1. Find
the average speed of water in the river Ganga.

Water flows through a horizontal tube of variable cross section (figure 13-E7). The area of cross section at A and B are 4 mm² and 2 mm² respectively. If 1 cc of water enters per second through A, find (a) the speed of water at A, (b) the speed of
water at B and (c) the pressure difference P_A – P_B.