Question

A steel ball of mass $0.1 \,kg$ falls freely from a height of $10\, m$ and bounces to a height of $5.4 \,m$ from the ground. If the dissipated energy in this process is absorbed by the ball, the rise in its temperature is (specific heat of steel $=460\, J - kg { }^{-10} \,C^{-1}, g=10 \,m s^{-2}$)

• A. $0.01^{\circ} C$
• B. $ 0.1^{\circ}C $
• C. $ 1^{\circ}C $
• D. $ 1.1^{\circ}C $

Answer 1

The Correct Option is B

According to energy conservation, change in potential energy of the ball, appears in the form of heat which raises the temperature of the ball. ie, \(m g\left(h_{1}-h_{2}\right)=m c . \Delta \theta\) \(\Rightarrow \Delta \theta=\frac{g\left(h_{1}-h_{2}\right)}{c}\) \(=\frac{10(10-5.4)}{460}=0.1^{\circ} C\)

Energy cannot be generated or destroyed, according to the law of conservation of energy. An isolated system has the same total energy when all sources of energy are taken into account. The fact that one type of energy may be changed into another means that energy never changes. The universe's many types of energy are all subject to the law of conservation of energy. 

A portion of an isolated system, like the cosmos, that experiences energy consumption or loss must also experience an equivalent amount of energy gain. Any system's energy may be calculated using the following equation: 

U_T = U_i + W + Q.

Where, 

A system's overall energy is referred to as U_T.

The initial energy of a system is referred to as U_i.

Q is the heat that the system gains or loses.

W is the work that the system does or produces.

Internal energy of a system changes when work is being done. This change in a system's internal energy may be computed using the equation below; 

ΔU = W + Q

where ΔU represents the system's internal energy change