Basic Science T...

An emergency vehicle travels $$10$$ miles at a speed of $$50$$ miles per hour. How fast must the vehicle travel on the return trip if the round-trip travel time is to be $$20$$ minutes?

An on jest is dropped in an unknown planet from height $$50\ m $$ it reaches the ground in $$2s$$ the acceleration due to gravity in this unknown planet is 

A boy aims a target at a horizontal distance of $$60\ m $$. If the muzzle speed of bullet is $$600\ m/s $$, then the height above the target which he should aim is 

The angular velocity of the body changes from $$ \omega_{1} $$ to $$ \omega_{2} $$ without applying torque but by changing moment of inertia. The ratio of initial radius of gyration to the final radius of gyration is :

A body is projected vertically upwards. The times corresponding to height $$H$$ while ascending and while descending are $$t_{1} $$ and $$t_{2} $$ respectively. Then the maximum height reached from the point of projection, is 

A physical quantity $$X$$ is given by $$X=\dfrac{a^{3} b^{2} d}{c^{1 / 2}},$$ the percentage error in the measurement of $$a, b, c$$ and dare $$1 \%, 3 \%, 2 \%$$ and $$4 \%$$ respectively. The maximum percentage error in the measurement of $$X$$ is

The side of a cube mesasured by a vernier calliper
whose 10  division of the veriner scale are equal to 8 divisions of main scale If the main scale reads 10 mm and second division of vernier scale coincides with one of the main scale division then the value of the cube in appropriate significant figures is (take 1 MSD = 1mm)

A uniform rod of length $$2l$$ is placed with one end in contact with the horizontal table and is then inclined at an angle $$\alpha $$ to the horizontal and allowed to fall. When it becomes horizontal, its angular velocity will be 

Find the acceleration of block of mass m. Assume pulleys are massless and frictionless.

The angular speed of a body changes from $$\omega_{0}$$ to $$\omega,$$ solely due to a change in its moment of inertia. The ratio of the radii of gyration is