MHT CET 2018 :: Physics :: General questions

• Physics - General questions

A mass attached to one end of a string crosses top-most point on a vertical circle with critical  speed, its centripetal acceleration when string becomes horizontal  will be (where, g= gravitational acceleration)

Answer:

Explanation:

 we know that,

 velocity of particle at top -most point on vertical circle,

 $(V_{top})= \sqrt{3rg}$    ...........(i)

 But centripetal acceleration (a_c)=$\frac{V^{2}}{r}$

 $\therefore$    $a_{c}=\frac{(\sqrt{3rg})^{2}}{r}$      [from Eq. (i)]

 $a_{c}=\frac{3rg}{r}$

 a_c  = 3g

A bomb at rest explodes into 3 parts of same mass . The momentum of two parts is -3 p $\hat{i}$ and 2p$\hat{j}$ , respectively . The magnitude of momentum of the third part is 

Answer:

Explanation:

According to the question , we can draw the following diagram. Now , the magnitude of momentum of the third part is given by

$p_{3}=\sqrt{(p_1^2)+(p_{2})^{2}}$

 $p_{3}=\sqrt{(-3p)^2)+(2p)^{2}}$

$p_{3}=\sqrt{9p^2+4p^{2}}$

$p_{3}=\sqrt{13p^{2}}$

$\therefore$     $p_{3}=\sqrt{13}p$

The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is l. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it, so that their centres coincide. If  both the rings are rotating  about the same axis, then loss in kinetic energy is 

Answer:

Explanation:

  According to the law of conservation of angular momentum, 

    l $\omega$  = constant

 Now, according  to the question,

$l_{1}\omega_{1}=l_{2}\omega_{2}$ or  $ k\omega= (2l) \omega_{2}$

 $\omega_{2}=\frac{\omega}{2}$

 New kinetic energy =  $[\frac{1}{2}l_{2}\omega_{2}^{2}]= \frac{1}{2}(2l)\times (\frac{\omega}{2})^{2}= \frac{l\omega^{2}}{4}$

 loss in kinetic energy (K_L)= K_i  - K_j

 =  $\frac{1}{2}l_{}\omega_{}^{2}-  \frac{l\omega^{2}}{4}=\frac{l\omega^{2}}{4}$

Magnetic susceptibility for a paramagnetic and diamagnetic materials is respectively

Answer:

Explanation:

 The magnetic susceptibility  of a magnetic  substance is defined as the ratio of intensity of magnetisation (l) to magnetic intensity (H)  , i.e,

  x= $\frac{l}{H}$

 For paramagnetic material, x is positive  and small (0  < x < ε ), where ε   is small positive number

 For diamagnetic meterial , x is negative and small  $(-1 \leq x \leq0)$ 

Asquare frame ABCD is formed by four identical rods each of mass m and length l, This frame is in

XY- plane such that side AB coincides with X-axis and side AD along Y- axis. The moment of inertia of the frame about X-axis is 

Answer:

Explanation:

In the given figure,

 $l=l_{AB}+l_{BC}+l_{CD}+l_{DA}=0+\frac{ml^{2}}{3}+ml^{2}+\frac{ml^{2}}{3}$

or  $l=\frac{5ml^{2}}{3}$

• Physics - General questions