Question

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in figure. The horizontal velocity of the block is -

• A. v
• B. $\frac { \mathrm { v } } { \sin \theta }$
• C. v sin q
• D. $\frac { \mathrm { v } } { \cos \theta }$

Answer 1

Answer: (B)

$\frac { \mathrm { v } } { \sin \theta }$

Answer 2

x² + y² = l²

$2 \mathrm { x } \frac { \mathrm { du } } { \mathrm { dt } }$ + 0 = 2l $\frac { \mathrm { d } \ell } { \mathrm { dt } }$ [y = constant]

or $\left| \frac { \mathrm { dx } } { \mathrm { dt } } \right| = \frac { \left| \frac { \mathrm { d } \ell } { \mathrm { dt } } \right| } { ( \mathrm { x } / \ell ) } = \frac { \mathrm { v } } { \sin \theta }$