Subjective Type

Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed $$\upsilon_1$$ and $$\upsilon_2$$, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and $$\upsilon_1 = 3 m/s$$ then $$\upsilon_2$$ in m/s is $$(g = 10 m/s^2)$$

Solution

$$K_{total} = K_{tr} + K_{rot}$$
$$= \dfrac{1}{2}mv^2 + \dfrac{1}{2}I\omega ^2$$
$$= \dfrac{1}{2}mv^2 + \dfrac{1}{2} ( \dfrac{mR^2}{2})(\dfrac{v}{R})^2$$
$$=\frac{3}{4}mv^2$$
Since velocity of both the discs are same at B , using conservation of energy,
$$\dfrac{3}{4}mv_1^2 + mg(30) = \dfrac{3}{4}mv_2^2 + mg(27)$$
Putting $$v_1=3$$ and solving
$$v_2 ^2 = 49$$
$$ \Rightarrow v_2 =7$$

SIMILAR QUESTIONS

If $$R=\left\{\left(x,y\right):y=2x\right\}$$ is a relation in $$A=\left\{1,2,3,4,6,7,8\right\}$$ then write all the elements of $$R$$

Let $$X=\left\{1,2,3,4\right\}$$.Determine whether $$f=\left\{\left(1,1\right),\left(2,3\right),\left(3,4\right),\left(4,1\right)\right\}$$ are functions from $$X$$ to $$X$$

Let the universal set U, be a set all students of your school, A is set of boys. B is the set of girls C is the set of students participating in sports. Describe the following set in words and represent them by the Venn diagram. $$B \cap C$$

If $$A = $${1,4,6}, $$B = $${3,6}, then find $$(A \cap B)$$

Find the number of whole numbers in the solution set of following $$x - 5 <-2$$

Find the solution of the following: If $$5x + 4 > 8x - 11$$, then $$x

Say true or false. The A.M. between $$(a-b)^2$$ and $$(a+b)^2$$ is $$a^2+b^2 $$.

Given a line I and a point P on it. How many lines can be drawn passing through the point P?

If lines $$l_1\, \perp\, l_2$$ and the the slope of $$l_1$$ is $$\dfrac{1}{2}$$, then the the slope of $$l_2$$ is .......... .

Contact Details