Basic Science T...

A particle is projected with a velocity v, so that its range on a horizontal plane is twice the greatest height attained. If g is acceleraction due to gravity, then its range is:

A heavy box with mass M 200 kg slides down a 4 m long ramp which makes $$30^o$$ with horizontal. There is a small friction force which performs work W-2250 J. The box had no initial velocity at the top of the ramp. Find the speed of the box (in m/s) at the bottom of the ramp.

A body slides down a smooth inclined plane of base $$x$$ meter. Find the angle of the plane so that the time taken by the body to reach the bottom of the plane is minimum 

A boat which can move with a speed of $$5\ m/s$$ relative to water crosses a river of width $$480\ m$$ flowing with a constant speed of $$4\ m/s$$. Find the time taken by the boat to cross the river along the path which is shortest. Find also the length of shortest path.

A 100 m long train crosses a man travelling at 5 km/h, in opposite direction in 7.2 seconds, then the velocity of train is:-

A cyclist goes round a circular path of circumference $$\pi \ m$$ in $$\sqrt 2\ s$$, the  angle made by him with the vertical will be 

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

In a vernier callipers , one scale division in x  cm , and n division  of the vernier scale coincide with (n -1) divisions of the main scale . The least count (in cm ) of  the callipers  is

Maximum percentage error in the measurement of 25.00 m is 

The dimension of heat capacity are