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### A body of mass 'm' dropped from a height 'h' ....

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8 \sqrt {gh}$. The value of work done by the air-friction is:

(A) -0.68 mgh
(B) 0.64 mgh
(C) mgh
(D) 1.64 mgh

Solution

Short Method

Air friction force is resistive force whose work-done must be negative. The only option with negative value is (A).

Detailed Method

Work done by all forces $W_{all} = \Delta K$

$\therefore W_{mg} + W_{air friction} = \frac {1}{2} mv^2 - 0$

$\Rightarrow W_{fr} = \frac {1}{2} m \times (0.8 \sqrt {gh} )^2 - mgh$

$\Rightarrow W_{fr} = 0.32 mgh - mgh = -0.68 mgh$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$