A block of mass $\mathrm{m}$ is placed on a triangular block of mass $M$, which in turn is placed on a horizontal surface as shown in figure. Assuming frictionless surfaces between the velocities of the triangular block when the smaller block reaches the bottom end.
Along x-direction ${ }^{a_{C O M}}=0$
$\Rightarrow \frac{m a_{x}-(M+m)\left(a_{2}\right)}{(M+m+m)}=0$
$\Rightarrow a_{2}=\frac{m a_{x}}{m+M}$
$m a=m g \sin \alpha$
$a_{x}=a \cos \alpha=g \sin \alpha \cos \alpha$
$a_{r}=$ resultant $=g \sin \alpha-a_{\alpha} \sin \alpha$
$=g \sin \alpha\left[\frac{M+m \sin ^{2} \alpha}{M+m}\right]$
Vertical distance travelled by $\frac{h}{\mathrm{~m}=\sin \alpha}=y$
Use law of kinematics,
$t=\sqrt{\frac{2 y}{a_{r}}}=\sqrt{\frac{2 h}{a_{r} \sin \alpha}}$
$\{$ velocity of $M$ block $\}$
$=\frac{m g \cos \alpha}{M+m} \sqrt{\frac{2 h \sin \alpha[M+m]}{g \sin \alpha \cdot\left[M+m \sin ^{2} \alpha\right]}}$
$=\sqrt{\frac{2 m^{2} g^{2} h \cos ^{2} \alpha}{(M+m)\left(M+m \sin ^{2} \alpha\right)}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,