$A$ magnetic needle lying parallel to a magnetic field is turned through $60^{\circ}$. The work done on it is $W$. The torque required to maintain the magnetic needle in the position mentioned above is

Which one of the following reactions occurs at the anode in the Castner process of extracting sodium metal?

When a body of mass $1.0\, kg$ is suspended from a certain light spring hanging vertically,its length increases by $5\, cm$. By suspending a $2.0\, kg$ block to the spring,if the block is pulled through $10\, cm$ and released,the maximum velocity in $m/s$ is: (Acceleration due to gravity $g = 10\, m/s^2$)

$A$ stone thrown upwards has its equation of motion $s = 490t - 4.9t^2$. Then the maximum height reached by it is

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then what is the set of possible values of $a$?

When a bucket is half full,the weight of the bucket and the water is $10 \ kg$. When the bucket is two-thirds full,the total weight is $11 \ kg$. What is the total weight (in $kg$),when the bucket is completely full?