11.

The escape velocity of a projectile on the earth's surface is 11.2 kms^-1 . A body is projected out with the thrice this speed. What is the speed of the body far away from the earth ? Ignore the presence of the sun and other planets. 

• 22.4 kms^-1

• 6.5 kms^-1

• 31.68 kms^-1

• 18.32 kms^-1

A body is at rest at x = 0 and t = 0, it starts moving in the positive X-direction with a constant acceleration. At the same instant, another body passes through x = O moving in the positive X-direction with a constant speed. The position of the first body is given by x₁ (t) after time t and that of second body by x₂ (t) after the same time interval. Which of the following graphs correctly describes (x_1 − x₂) as a function of time t ?

Two body are standing at the ends A and B of a ground, where AB = a . The boy at B starts running in a direction perpendicular to AB with velocity v₁ . The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

• $\frac{\mathrm{a}}{\sqrt{{\mathrm{v}}^2 + {{\mathrm{v}}_1}^2}}$

• $\frac{{\mathrm{a}}^2}{\sqrt{{\mathrm{v}}^2 - {{\mathrm{v}}_1}^2}}$

• $\frac{\mathrm{a}}{\mathrm{v} - {\mathrm{v}}_1}$

• $\frac{\mathrm{a}}{\mathrm{v} + {\mathrm{v}}_1}$

A body of mass M at rest explodes into three pieces, two of which are of mass $\frac{\mathrm{M}}{4}$ each are thrown off in perpendicular directions with velocities of 3m/s and 4m/s respectively. The third piece will be thrown off with a velocity of

• 1.5 m/s

• 2.0 m/s

• 2.5 m/s

• 3.0 m/s

Three points charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{2{\mathrm{q}}^2}{\mathrm{a}}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{{\mathrm{q}}^2}{2\mathrm{a}}$

• $\frac{1}{4{\mathrm{\pi \epsilon }}_0} \frac{8\mathrm{q}}{{\mathrm{a}}^2}$

• 0

Two tunning forks A and B, produce notes of frequencies 258 Hz and 262 Hz. An unknown note sounded with A produces certain beats. When the same note is sounded with B. The beat frequency gets doubled. The unknown frequency is

• 250 Hz

• 252 Hz

• 254 Hz

• 256 Hz

Consider two containers P and Q containing identical gases at same temperature, pressure and volume. The gas in container P is compressed to half of its original volume isothermally while the gas in container Q is compressed to half of its original value adibatically. The ratio of final pressure of gas is

• $2^{\mathrm{\gamma }-1}$

• ${\left(\frac{1}{2}\right)}^{\mathrm{\gamma }-1}$

• ${\left(\frac{1}{1 - \mathrm{\gamma }}\right)}^2$

• ${\left(\frac{1}{\mathrm{\gamma } - 1}\right)}^2$

Springs of spring constants K, 2K,4K, 8K...are connected in series.A mass m kg is attached to the lower end of the last spring and the system is allowed to vibrate. The time period of oscillations is (Given, m= 40 g and k =2.0 N-cm^-1)

• 2.12 s

• 0.126 s

• 1.26 s

• 0.0126 s

Air of density 1.3 kg/m³ flows horizontally with a speed 106 km/h. A house has a plane roof of area 40 m². Find the magnitude of aerodynamic lift on the roof.

• 4.22 × 10⁵ N

• 2.25 × 10⁴ N

• 4.22 × 10³ N

• 2.25 × 10⁶ N

The length of a steel rod is 5 cm longer than that of a brass rod. If this difference in their lengths is to remain the same at all temperatures, then the length of brass rod will be (coefficient of linear expansion for steel and brass are 12 x 10^-6 /°C and 1.8 × 10^-6 /°C 

• 20 cm

• 15 cm

• 5 cm

• 10 cm