To cover a population of 20 lakh, a transmission tower should have a height (Radius of earth = 6400 km, populatton per square km=1000)

• 25 m

• 50 m

• 75 m

• 100 m

Three blocks of masses m₁ m₂ and m₃ are connected by massless string as shown kept on a frictionless table.

They are pulled with a force T₃ = 40 N. If m₁ = 10 kg, m₂ = 6 kg and m₃ = 4 kg, the tension T₂ will be

• 20 N

• 40 N

• 10 N

• 32 N

If the two vectors $\overrightarrow{\mathrm{A}} = 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{B}} = \hat{\mathrm{i}} + 2\hat{\mathrm{j}} - \mathrm{n}\hat{\mathrm{k}}$ are perpendicular then the value of n is

• 1

• 2

• 3

• 4

4.

A stone of mass m tied to a string of length l is rotating along a circular path with constant speed v. The torque on the stone is

• mlv

• $\frac{\mathrm{mv}}{\mathrm{l}}$

• zero

• mv²l

LANDSAT series of satellites move in near polar orbits at an altitude of

• 3600 km

• 3000 km

• 918 km

• 512 km

A boat travels 50 km east, then 120 km North and finally it comes back to the starting point through the shortest distance. The total time of journey is 3 h. What is the average velocity, in km h^-1 over the entire trip ?

• zero

• 100

• 17

• 33.33

Potential energy in a spring when stretched by 2 cm is U. Its potential energy, when stretched by 10 cm is

• $\frac{\mathrm{U}}{25}$

• $\frac{\mathrm{U}}{5}$

• 25 U

• 5 U

A toy cyclist completes one round of a square track of side 2 m in 40 s. What will be the displacement at the end of 3 min ?

• 52 m

• zero

• 16 m

• $2\sqrt{2} \mathrm{m}$

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is

• $\sqrt{3} \mathrm{v}$

• $\sqrt{2} \mathrm{v}$

• v

• $\sqrt{5} \mathrm{v}$

Two trains, each of length 200 m are runmng on parallel tracks. One overtakes the other in 20 s and one crosses the other in 10 s. The velocities of the two trains are

• 5 m/s, 10 m/s

• 10 m/s, 30 m/s

• 15 m/s, 5 m/s

• 20 m/s, 21 m/s