Water falls from a height of 60 m at the rate of 15 kg /s to operate a turbine. The losses due to frictional 

• 8.1 kW

• 10.2 kW

• 12.3 kW

• 12.3 kW

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

The diagrams below show regions of equipotentials

A positive charge is moved from A to B in each diagram.

• Maximum work is required to move q in figure (c).

• In all the four cases the work done is the same.

• Minimum work is required to move q in figure (a).

• Minimum work is required to move q in figure (a).

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is

• (i) – 10 J (ii) –8.25 J

• (i) 1.25 J (ii) –8.25 J

• (i) 100 J (ii) 8.75 J

• (i) 100 J (ii) 8.75 J

If force $\overrightarrow{\mathrm{F}}=5\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ makes a displacement of $\overrightarrow{\mathrm{s}}=6\hat{\mathrm{i}}-5\hat{\mathrm{k}}$work done by the force is

• 10units

• $122\sqrt{5}$units

• $5\sqrt{122}\mathrm{units}$

• 20units

$$\begin{gathered} \mathrm{A} \mathrm{particle} \mathrm{moves} \mathrm{from} \mathrm{postion} \\ \overrightarrow{{\mathrm{r}}_1}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}-6\hat{\mathrm{k}} \mathrm{to} \mathrm{position} \overrightarrow{ {\mathrm{r}}_2}=14\hat{\mathrm{i}}+13\hat{\mathrm{j}}+9\hat{\mathrm{k}} \mathrm{under} \mathrm{action} \mathrm{of} \mathrm{force} \\ \overrightarrow{\mathrm{F}}=4\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}} \mathrm{N}. \mathrm{The} \mathrm{work} \mathrm{done} \mathrm{will} \mathrm{be} \end{gathered}$$

• 100J

• 50J

• 200J

• 75J

The work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth plane inclined at an angle of 15° with the horizontal is

• 9.82 kJ

• 89 kJ

• 4.35 kJ

• 5.17 kJ

If the heat of 110 J is added to a gaseous system, whose internal energy is 40 J, then the amount of external work done is

• 180J

• 70J

• 110J

• 30J

109.

Amount of work which can be obtained from 200 cal heat, will be

• 280 J

• 800 J

• 420 J

• 840 J

The spring extends by x on loading, then energy stored by the spring is (if T is the tension in spring and k is
spring constant

• $\frac{{\mathrm{T}}^2}{2\mathrm{k}}$

• $\frac{{\mathrm{T}}^2}{2{\mathrm{k}}^2}$

• $\frac{2k}{{\mathrm{T}}^2}$

• $\frac{2{\mathrm{T}}^2}{k}$