Q: The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is-

Work done in stretching a spring to x length is \$W=\dfrac{1}{2}kx^2\$\$\therefore\$ Work one in stretching from \$x_1\$ to \$x_2\$ is proportional to \$W \propto x_2^2-x_1^2\$hence \$\dfrac{W_{20,30}}{W_{10,20}}=\dfrac{500}{300}\$so, 10 to 20 takes less work when compared to 20 to 30.

Q: A ball tied to a string is swung in a vertical circle. Which of the following remains constant?

Earth's pull on the ball remains constant \$(W=mg)\$.Tension in the string changes along the vertical circular path.Speed of the ball changes as sum of kinetic energy and potential energy remains constant during motion.Speed changes, hence, centripetal force changes.

Q: A lighter body moving with a velocity \$v\$ collides with a heavier body at rest. Then :

In a collision system where \$m_1\$ moves with \$u_1\$ initially and \$m_2\$ is at rest with \$m_2 >>> m_1\$.Let the final velocity of \$m_1\$ be \$v_1\$ and \$m_2\$ be \$v_2\$.Assumption: Let the collision be elastic. Using linear momentum conservation and equation for coefficient of restitution,\$ m_1u_1 = m_2v_2 + m_1v_1 \$\$ v_2 - v_1 = u_1 \$We get \$ v_1 = \dfrac {m_1 - m_2 }{m_1 + m_2} u_1 \$\$ v_2 = \dfrac {2m_1}{m_1 + m_2} u_1 \$Using \$m_2 >>> m_1,\$ we get \$ v_1 = -u_1 \$ and \$ v_2 = 0 \$.

Q: The K.E. of a body can be increased maximum by doubling its:

\$ K.E = \dfrac{1}{2}mv^2\$\$ K.E \propto m \$ & \$ K.E \propto v^2 \$So doubling mass will double the kinetic energy and doubling speed will make kinetic energy \$4\$ times.\$ \therefore \$ The K.E. of a body can be increased maximum by doubling its speed.

Q: A certain force acting on a body of mass 2kg increase its velocity from 6m/s to 15 m/s in 2s. The work done by the force during this interval is ?

we know that v=u+at15=6+a(2)\$a= 4.5 m/s^2\$\$s=ut+0.5at^2= 6(2)+ 0.5(4.5)(4)= 21 m\$\$W= mas= 2(4.5)(21)= 189 J\$

Q: A particle moves under the effect of a force \$F=Cx\$ form \$x=0\$ to \$x=x_{1}\$. The work done in the process is-

Similar to a spring with neutral point at x=0\$W = \int \bar F.\bar ds = \int_0^{x_1} Cx dx = 0.5Cx_1^2\$

Q: A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

\$\textbf{Step 1: Energy Conservation [Ref. Fig.]}\$\$\text{Dependence on m}\$Let \$u\$ be the minimum speed required at \$B\$.Apply energy conservation between point \$A\$ and \$B\$ we get \$KE_A + PE_A = KE_B + PE_B\$Taking point \$A\$ as zero potential level \$\Rightarrow\$ \$\dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} mv^2 \$ \$....(1)\$From equation \$1\$, we observe that mass \$m\$ is cancelled on both sides.\$\Rightarrow u\$ is independent of \$m\$.\$\textbf{Steo 2: Solving Equation}\$\$\text{Dependence on R}\$At highest point, Tension will be zero for minimum velocity\$\Rightarrow\$ gravitational pull will provide necessary centripetal force \$\Rightarrow mg = \dfrac{mv^2}{R}\$ \$\Rightarrow v^2 = Rg\$ .... Putting in equation \$(1)\$We get, \$\dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} m (Rg)\$ \$\Rightarrow u = \sqrt{5Rg}\$\$\Rightarrow u\$ is proportional to the square root of \$R\$.Hence option \$B\$ is correct.

Question 1

The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is-

Accepted Answer

Work done in stretching a spring to x length is $W=\dfrac{1}{2}kx^2$$\therefore$ Work one in stretching from $x_1$ to $x_2$ is proportional to $W \propto x_2^2-x_1^2$hence $\dfrac{W_{20,30}}{W_{10,20}}=\dfrac{500}{300}$so, 10 to 20 takes less work when compared to 20 to 30.

Question 2

A ball tied to a string is swung in a vertical circle. Which of the following remains constant?

Accepted Answer

Earth's pull on the ball remains constant $(W=mg)$.Tension in the string changes along the vertical circular path.Speed of the ball changes as sum of kinetic energy and potential energy remains constant during motion.Speed changes, hence, centripetal force changes.

Question 3

A lighter body moving with a velocity $v$ collides with a heavier body at rest. Then :

Accepted Answer

In a collision system where $m_1$ moves with $u_1$ initially and $m_2$ is at rest with $m_2 >>> m_1$.Let the final velocity of $m_1$ be $v_1$ and $m_2$ be $v_2$.Assumption: Let the collision be elastic. Using linear momentum conservation and equation for coefficient of restitution,$ m_1u_1 = m_2v_2 + m_1v_1 $$ v_2 - v_1 = u_1 $We get $ v_1 = \dfrac {m_1 - m_2 }{m_1 + m_2} u_1 $$ v_2 = \dfrac {2m_1}{m_1 + m_2} u_1 $Using  $m_2 >>>  m_1,$  we get $ v_1 = -u_1 $ and $ v_2 = 0 $.

Question 4

The K.E. of a body can be increased maximum by doubling its:

Accepted Answer

$ K.E = \dfrac{1}{2}mv^2$$ K.E \propto m $    &    $ K.E \propto v^2 $So doubling mass will double the kinetic energy and doubling speed will make kinetic energy $4$ times.$ \therefore $ The K.E. of a body can be increased maximum by doubling its speed.

Question 5

A certain force acting on a body of mass 2kg increase its velocity from 6m/s to 15 m/s in 2s. The work done by the force during this interval is ?

Accepted Answer

we know that v=u+at15=6+a(2)$a= 4.5 m/s^2$$s=ut+0.5at^2= 6(2)+ 0.5(4.5)(4)= 21 m$$W= mas= 2(4.5)(21)= 189 J$

Question 6

Name the type of energy (kinetic energy $K$ or potential energy $U$) possessed in a compressed spring:

Accepted Answer

When you compress a spring, it possess potential energy. The force of compression is proportional to the compression, according to Hooke's Law. Releasing the spring turns the potential energy into kinetic energy. The spring can be then used to propel some object.

Question 7

Energy equals of a mass of one microgram in kilo joules is

Accepted Answer

GivenEnergy of 1 microgram=?SolutionWe will use Energy mass equivalence$E=mc^{2}$$E=10^{-6}kg\times (3 \times10^{8})^{2}m/s^{2}$$E=9 \times 10^{10}J$Option $A$ is  correct.

Question 8

A particle moves under the effect of a force $F=Cx$ form $x=0$ to $x=x_{1}$. The work done in the process is-

Accepted Answer

Similar to a spring with neutral point at x=0$W = \int \bar F.\bar ds = \int_0^{x_1} Cx dx = 0.5Cx_1^2$

Question 9

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

Accepted Answer

$\textbf{Step 1: Energy Conservation     [Ref. Fig.]}$$\text{Dependence on m}$Let $u$ be the minimum speed required at $B$.Apply energy conservation between point $A$ and $B$ we get              $KE_A + PE_A = KE_B + PE_B$Taking point $A$ as zero potential level    $\Rightarrow$            $\dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} mv^2 $  $....(1)$From equation $1$, we observe that mass $m$ is cancelled on both sides.$\Rightarrow u$ is independent of $m$.$\textbf{Steo 2: Solving Equation}$$\text{Dependence on R}$At highest point, Tension will be zero for minimum velocity$\Rightarrow$ gravitational pull will provide necessary centripetal force           $\Rightarrow mg = \dfrac{mv^2}{R}$           $\Rightarrow v^2 = Rg$ .... Putting in equation $(1)$We get, $\dfrac{1}{2} mu^2 = mg (R + R) + \dfrac{1}{2} m (Rg)$           $\Rightarrow u = \sqrt{5Rg}$$\Rightarrow u$ is proportional to the square root of $R$.Hence option $B$ is correct.

Question 10

Complete the following sentence: The kinetic energy of a body is the energy by virtue of its______ .

Accepted Answer

The kinetic energy of a body is the energy by virtue of its motion. This is the definition of kinetic energy. If it has motion then it will have velocity, hence kinetic energy exists.$ K.E = \dfrac{1}{2}mv^2 $

Work Energy And Power

Physics
17820 Views

The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is-

A ball tied to a string is swung in a vertical circle. Which of the following remains constant?

A lighter body moving with a velocity $v$ collides with a heavier body at rest. Then :

The K.E. of a body can be increased maximum by doubling its:

A certain force acting on a body of mass 2kg increase its velocity from 6m/s to 15 m/s in 2s. The work done by the force during this interval is ?

Name the type of energy (kinetic energy $K$ or potential energy $U$ ) possessed in a compressed spring:

Energy equals of a mass of one microgram in kilo joules is

A particle moves under the effect of a force $F = C x$ form $x = 0$ to $x = x_{1}$ . The work done in the process is-

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

Complete the following sentence:
The kinetic energy of a body is the energy by virtue of its______ .

Work Energy And Power

Physics 17820 Views

The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is-

A ball tied to a string is swung in a vertical circle. Which of the following remains constant?

A lighter body moving with a velocity v collides with a heavier body at rest. Then :

The K.E. of a body can be increased maximum by doubling its:

A certain force acting on a body of mass 2kg increase its velocity from 6m/s to 15 m/s in 2s. The work done by the force during this interval is ?

Name the type of energy (kinetic energy K or potential energy U) possessed in a compressed spring:

Energy equals of a mass of one microgram in kilo joules is

A particle moves under the effect of a force F=Cx form x=0 to x=x1​. The work done in the process is-

A stone tied to a string is rotated in a vertical circle. The minimum speed with which the stone has to be rotated in order to complete the circle :

Complete the following sentence: The kinetic energy of a body is the energy by virtue of its______ .

Physics
17820 Views

A lighter body moving with a velocity $v$ collides with a heavier body at rest. Then :

Name the type of energy (kinetic energy $K$ or potential energy $U$ ) possessed in a compressed spring:

A particle moves under the effect of a force $F = C x$ form $x = 0$ to $x = x_{1}$ . The work done in the process is-

Complete the following sentence:
The kinetic energy of a body is the energy by virtue of its______ .