A person is driving a vehicle at uniform speed of 5 ms^-1 on a level curved track of radius 5 m. The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed ? Take g = 10 ms^-2.

• A person will slip, if v² = 5 m²s^-2

• A person will slip, if v² > 5 m²s^-2

• A person will slip, if v² < 5 m²s^-2

• A person will not slip, if v² > 5 m²s^-2

A stone is thrown vertically at a speed of 30 ms^-1 taking an angle of 45° with the horizontal. What is the maximum height reached by the stone ? Take g = 10 ms^-2.

• 30 m

• 22.5 m

• 15 m

• 10 m

A force $\mathrm{F} = 5\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - 5\hat{\mathrm{k}}$ acts on a particle whose position vector is $\mathrm{r} = \hat{\mathrm{i}} - 2\hat{\mathrm{j}} + \hat{\mathrm{k}}$. What is the torque about the origin ?

• $8\hat{\mathrm{i}} + 10\hat{\mathrm{j}} + 12\hat{\mathrm{k}}$

• $8\hat{\mathrm{i}} + 10\hat{\mathrm{j}} - 12\hat{\mathrm{k}}$

• $8\hat{\mathrm{i}} - 10\hat{\mathrm{j}} - 8\hat{\mathrm{k}}$

• $10\hat{\mathrm{i}} - 10\hat{\mathrm{j}} - \hat{\mathrm{k}}$

What is a period of revolution of the earth satellite ? Ignore the height of satellite above the surface of the earth. Given : 

1. The value of gravitational acceleration g = 10 ms^-2
2. Radius of the earth, R_E = 6400 km (Take π = 3.14)

• 85 min

• 156 min

• 83.73 min

• 90 min

A period of geostationary satellite is

• 24 h

• 12 h

• 30 h

• 48 h

A rotating wheel changes angular speed from 1800 rpm to 3000 rpm to 20 s. What is the angular acceleration assuming to be uniform ?

• $60 \mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-2}$

• $90 \mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-2}$

• $2\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-2}$

• $40 \mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-2}$

An aeroplane executes a horizontal loop at a speed of 720 km/h with its wings banked at 45°. What is the radius of the loop ? Take g = 10 ms^-2

• 4 km

• 4.5 km

• 7.2 km

• 2 km

A body having a moment of inertia about its axis of rotation equal to 3 kg m² is rotating with angular velocity of 3 rad s^-1. Kinetic energy of this rotating body is same as that of a body of mass 27 kg moving with a velocity v. The value of v is

• 1 ms^-1

• 0.5 ms^-1

• 2 ms^-1

• 1.5 ms^-1

A physical quantity Q is found to depend on observables x, y and z obeying relation $\mathrm{Q} = \frac{{\mathrm{x}}^3{\mathrm{y}}^2}{\mathrm{z}}$. The percentage error in the measurements of x, y and z are 1 %, 2 % and 4 % respectively. What is percentage error in the quantity Q ? 

• 4 %

• 3 %

• 11 %

• 1 %

Which of the following is not a vector quantity ?

• Weight

• Nuclear spin

• Momentum

• Potential energy