(B) Given: mass $m = 0.1 \ kg$, change in momentum $\Delta p = 2 \ kg \ m/s$, time $t = 1 \ s$, $g = 10 \ m/s^2$.Since $\Delta p = F_{net} \times t$,

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The tension in the string is $3 \ N$

(B) Given: mass $m = 0.1 \ kg$, change in momentum $\Delta p = 2 \ kg \ m/s$, time $t = 1 \ s$, $g = 10 \ m/s^2$.Since $\Delta p = F_{net} \times t$, we have $F_{net} = \frac{\Delta p}{t} = \frac{2}{1} = 2 \ N$.For the block, the net force is $T - mg = F_{net}$, where $T$ is the tension in the string. Since the string is massless and the pulley is frictionless, $T = F$.Thus, $F - mg = 2 \ N \Rightarrow F - (0.1 \times 10) = 2 \Rightarrow F - 1 = 2 \Rightarrow F = 3 \ N$.So, the tension in the string is $T = F = 3 \ N$.Acceleration $a = \frac{F_{net}}{m} = \frac{2}{0.1} = 20 \ m/s^2$.Displacement $S = \frac{1}{2}at^2 = \frac{1}{2} \times 20 \times (1)^2 = 10 \ m$.Work done by tension $W_T = T \times S = 3 \times 10 = 30 \ J$.Work done against gravity $W_g = mg \times S = (0.1 \times 10) \times 10 = 10 \ J$.

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Medium

$A$ block of mass $m(=0.1 \ kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force $F$ in the vertically downward direction. The linear momentum of the block increases by $2 \ kg \ m/s$ in $1 \ s$ after the block starts from rest. Then, (given $g=10 \ m/s^2$):

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A
The tension in the string is $F$
B
The tension in the string is $3 \ N$
C
The work done by the tension on the block is $20 \ J$ during this $1 \ s$
D
The work done against the force of gravity is $1 \ J$

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

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$A$ mass of $10 \, g$ moving with a velocity of $100 \, cm/s$ strikes a pendulum bob of mass $10 \, g$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10 \, m/s^2)$.

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State if each of the following statements is true or false. Give reasons for your answer.
$(a)$ In an elastic collision of two bodies,the momentum and energy of each body is conserved.
$(b)$ Total energy of a system is always conserved,no matter what internal and external forces on the body are present.
$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.
$(d)$ In an inelastic collision,the final kinetic energy is always less than the initial kinetic energy of the system.

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$A$ body of mass $m$ is dropped from a height of $h$. Simultaneously,another body of mass $2m$ is thrown vertically upward with such a velocity $v$ that they collide at a height $h/2$. If the collision is perfectly inelastic,the velocity at the time of collision with the ground will be:

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Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially, $S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision, $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision:

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$A$ simple pendulum of length $L = \frac{10}{3} \text{ m}$ with a bob of mass $M = 3m$ is hanging freely from a rigid support. $A$ bullet of mass $m$ is fired with a velocity $u = 50 \text{ ms}^{-1}$ from the ground at an angle $\theta$ with the horizontal. When the bullet is at its highest point of its trajectory,it collides head-on with the bob of the pendulum and gets embedded in the bob. After collision,if the pendulum moves through a maximum angle of $120^{\circ}$,then the value of $\theta$ is $(g = 10 \text{ ms}^{-2})$.

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$A$ mass of $10 \, g$ moving with a velocity of $100 \, cm/s$ strikes a pendulum bob of mass $10 \, g$. The two masses stick together. The maximum height reached by the system now is ............... $cm$ $(g = 10 \, m/s^2)$.

$A$ body of mass $m$ is dropped from a height of $h$. Simultaneously,another body of mass $2m$ is thrown vertically upward with such a velocity $v$ that they collide at a height $h/2$. If the collision is perfectly inelastic,the velocity at the time of collision with the ground will be:

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