Download App

STD 11 - 6. system of particles and rotational motion — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. system of particles and rotational motion4 Marks
MCQ
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
  • A
    the heavier sphere reaches the bottom first
  • B
    the bigger sphere reaches the bottom first
  • ✓
    the two spheres reach the bottom together
  • D
    the information given is not sufficient to tell which sphere will reach the bottom first.
✓

Answer

Correct option: C.
the two spheres reach the bottom together
c
(c)

Since acceleration of a body during rolling without slipping, on an inclined plane of angle $\theta$ is given by

$a=\frac{g \sin \theta}{1+\frac{K^2}{R^2}}$, where $K$ is radius of gyration.

For solid sphere, $\frac{ K ^2}{ R ^2}=\frac{2}{5}$

Thus, $a=\frac{5}{7} g \sin \theta$

So, acceleration is independent of both mass and radius. Both spheres will reach bottom together.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A source of sound emitting a note of frequency $200 Hz$ moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$, the apparent frequency heard by the observer is .... $Hz$
→
A charged particle with specific charge $S$ moves undeflected through a region of space containing mutually perpendicular uniform electric and magnetic fields $E$ and $B$ . When electric field is switched off, the particle will move in a circular path of radius
→
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?

$(1)$ The dimension of force is $L ^{-3}$

$(2)$ The dimension of energy is $L ^{-2}$

$(3)$ The dimension of power is $L ^{-5}$

$(4)$ The dimension of linear momentum is $L ^{-1}$

→
An aeroplane flying $490 \,m$ above ground level at $100\, m/s$, releases a block. How far on ground will it strike ......... $km$
→
The force between two charges $0.06\,m$ apart is $5\,N$. If each charge is moved towards the other by $0.01\,m$, then the force between them will become.........$N$
→
Match the List-I with List-II
List-IList-II
A.Triatomic rigid gasI.$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}$
B.Diatomic non-rigid gasII.$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{7}{5}$
C.Monoatomic gasIII.$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3}$
D.Diatomic rigid gasIV.$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{9}{7}$
Choose the correct answer from the options given below :
→
The self produced $emf$ of a coil is $25\,volts$. When the current in it is changed at uniform rate from $10\,A$ to $25\, A$ in $1\,s$, the change in the energy of the inductance is......$J$
→
Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will be
→
$1\,\, kg$ of ice at $-10^o C$ is mixed with $4.4\,\, kg$ of water at $30^o C$. The final temperature of mixture is ........$^oC$ (specific heat of ice is $2100\,\,J/kg/k$)
→
A string fixed at both ends resonates at a certain fundamental frequency. Which of the following adjustments would not affect the fundamental frequency?
→