A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. The speed of the system, will be

• 3v

• $\frac{\mathrm{v}}{2}$

• $\frac{\mathrm{v}}{3}$

• 2v

The dimensions of gravitational constant are

• $\left[{\mathrm{ML}}^3{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^2\right]$

• $\left[{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right]$

A stone is thrown with an initial speed of 4.9m/s from a bridge in vertically upward direction.It falls down in water after 2sec. The height of bridge is

• 24.7m

• 19.8 m

• 9.8 m

• 4.9 m

A ball of mass 10 g moving with acceleration of 20 m/s² is hit by a force which acts on it for 0.1 sec. The impulsive force is

• 1.2Ns

• 0.3Ns

• 0.1Ns

• 0.5Ns

The earth of mass =6×10²⁴ kg revolves around the sun with an angular velocity of 2×10^-7 rad/s in a circular orbit of radius 1.5×10⁸ km. The force exerted by the sun on earth is

• 6×10¹⁹ N

• 18×10²⁵ N

• 36×10²¹ N

• 27×10³⁹ N

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

• 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

The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance 5×10¹¹m will be (charge on electron =1.6×10^-19 C, mass of electron =9.1×10^-31 kg, mass of proton =1.6×10^-27 kg, G=6.7×10^-11 Nm²/kg² )

• 2.36×10³⁹

• 2.36×10⁴⁰

• 2.36×10⁴¹

• 2.34×10⁴²

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

• 280 J

• 800 J

• 420 J

• 840 J