JEE 2014 :: Main 2014 :: Physics 2014

• Main 2014 - Physics 2014
• Main 2014 - Chemistry 2014
• Main 2014 - Mathematics 2014

A mass m supported by a massless string wound around a uniform hollow cylinder pf mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

Answer:

Explanation:

 For the mass m, mg-T=ma

 As we know, a= Rα

 So,   $mg-T=mR\alpha$ .............(i)

 Torque about centre of pully

 $T \times R=mR^{2}\alpha$ .........(ii)

 From Eqs.(i) and (ii) , we get

          $a=\frac{g}{2}$

  Hence, the acceleration with the mass of  a body fall is   $\frac{g}{2}$

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n  times that taken by it to reach the highest point of its path. The relation between H, u and n is 

Answer:

Explanation:

 Time taken to reach the maximum height

             t₁=u/g

If t₂ is the time taken to hit the ground,

i.e,    $-H=ut_{2}-\frac{1}{2}gt^{2}$

 But               t₂=nt₁                  [Given]

So, $-H=u\frac{nu}{g}-\frac{1}{2}g\frac{n^{2}u^{2}}{g^{2}}$

       $-H=\frac{nu^{2}}{g}-\frac{1}{2}\frac{n^{2}u^{2}}{g}$

   $\Rightarrow$                 $ 2gH=nu^{2}(n-2)$

The current-voltage relation of diode is given by  $I=(e^{1000V/T}-1)mA$, where the applied voltage V is in volt and the temperature T is in kelvin. If a student makes an error measuring the current of 5 mA at 300K, What will be the error in the value of current in m A?

Answer:

Explanation:

Given,   $I=(e^{1000V/T}-1)mA$ 

 $dV=\pm0.01V $

$T=300K\Rightarrow mA$

So,       $I= e^{1000V/T}-1$

$I+1= e^{1000V/T}$
Taking log onboth sides , we get

       log(I+1)= $\frac{1000V}{T}$

On differentiating,    $\frac{dI}{I+1}=\frac{1000}{T}dV$

$dI= \frac{1000}{T}\times (I+1)dV$

$\Rightarrow dI= \frac{1000}{300}\times (5+1)0.01=0.2mA$

So, error in the value of current is 0.2 mA

• Main 2014 - Physics 2014
• Main 2014 - Chemistry 2014
• Main 2014 - Mathematics 2014