A sphere is accelerated upwards with the help of a cord whose breaking strength is five times its weight. The maximum acceleration with which the sphere can move up without cord breaking is

The correct option is 4g.

To find the maximum acceleration with which the sphere can move upwards without the cord breaking, we can analyze the forces acting on the sphere.

Let the mass of the sphere be $m$ and the acceleration due to gravity be $g$. The weight of the sphere acting vertically downwards is:
$W=mg$

The breaking strength of the cord is the maximum tension $T_{\text{max}}$ it can support. We are given that the breaking strength is five times the weight of the sphere:
$T_{\text{max}}=5mg$

When the sphere is accelerated upwards with an acceleration $a$, two forces act on it: the upward tension $T$ in the cord and the downward force of gravity (weight) $m$$g$.

Applying Newton's second law of motion for the upward direction:
$T-mg=ma$
$T=m(g+a)$

The maximum acceleration $a_{\text{max}}$ occurs when the tension in the cord reaches its maximum limit $T_{\text{max}}$:
$T_{\text{max}}=m(g+a_{\text{max}})$

Substitute the expression for $T_{\text{max}}$ into the equation:
$5mg=m(g+a_{\text{max}})$

Divide both sides by the mass $m$:
$5g=g+a_{\text{max}}$

Solving for $a_{\text{max}}$:
$a_{\text{max}}=4g$

Thus, the maximum acceleration with which the sphere can move up without the cord breaking is $4g$.